Macbook Pro Does Not Start Up - Stuck at "No Entry" Sign

Question

Hello,
I've been dealing with this hours, so at last I decided to get help from the community.
Let me explain the issue first.
I have checked Software Update, and there was two updates. First one was Java and the other one was EFI Update 2.7. I don't remember the Java update version. After I applied the update, the MBP rebooted itself as it should do; bu the problem occured at that reboot. OSX tried to start up three times, like as it was failing to install the updates after reboot. And at the fourth time, after a few minutes the Apple logo turned into a "No Entry Sign". And it stuck like that. Now, the MBP cannot boot normally, I can only run it on safe mode.
I have reset PRAM.
As far as I read about the issue over the boards, the problem occurs to be an HDD problem. Yet I can run the OSX in safe mode, which bugs me. So I downloaded SMART Utility to check the HDD. It says there is 1 Pending Bad Sector, and 1 Removed Bad Sector.
What do I do now, any solutions you can offer?
This is the log export from SMART Utility if you wish to check it.
location: /dev/disk0
partition count: 1
partitions: Caprica HQ,
SMART Support: Supported
Last SMART Error: *not set*
Model Family: Seagate Momentus 5400.6
Model: ST9500325ASG
Serial Number: 5VELJHP6
Firmware Version: 0009APM1
Capacity: 500 GB
ATA Version: 8
ATA Standard: ATA-8-ACS revision 4
Health: Failing
Overall Health: PASSED
Offline Data Status: 0
Self Test Status: 0
Offline Data Collection Time: 0
Data Collection Capabilities: 73
SMART Capabilities: 3
Error Logging Capabilities: 1
Short Self Test Time: 1
Long Self Test Time: 139
Conveyance Self Test Time: 2
Attribute Log Revision: 10
Attribute Count: 22
Attributes:
ID#   ATTRIBUTE NAME                         FLAG       VALUE   WORST   THRESH  TYPE         UPDATED     FAILED    RAW VALUE
1     Raw Read Error Rate                    0x000E     117     099     006     Old age      Always      Never     141585185
3     Spin Up Time                           0x0003     100     100     000     Pre-fail     Always      Never     0
4     Start/Stop Count                       0x0032     100     100     020     Old age      Always      Never     18
5     Reallocated Sector Count               0x0033     100     100     036     Pre-fail     Always      Never     0
7     Seek Error Rate                        0x000F     100     253     030     Pre-fail     Always      Never     595148
9     Power On Hours                         0x0032     100     100     000     Old age      Always      Never     622
10    Spin Retry Count                       0x0013     100     100     097     Pre-fail     Always      Never     0
12    Power Cycle Count                      0x0032     100     100     020     Old age      Always      Never     366
184   End-to-End Errors                      0x0032     100     100     099     Old age      Always      Never     0
187   Reported Uncorrectable Errors          0x0032     090     090     000     Old age      Always      Never     10
188   Command Timeout                        0x0032     100     100     000     Old age      Always      Never     0
189   High Fly Writes                        0x003A     100     100     000     Old age      Always      Never     0
190   Airflow Temperature Celsius            0x0022     071     061     045     Old age      Always      Never     29
191   G-Sense Error Rate                     0x0032     100     100     000     Old age      Always      Never     99
192   Power Off Retract Count                0x0032     100     100     000     Old age      Always      Never     85
193   Load Cycle Count                       0x0032     083     083     000     Old age      Always      Never     34546
194   Temperature Celsius                    0x0022     029     040     000     Old age      Always      Never     29
195   Hardware ECC Recovered                 0x001A     051     043     000     Old age      Always      Never     141585185
197   Current Pending Sector Count           0x0012     100     100     000     Old age      Always      Never     1
198   Offline Uncorrectable Sector Count     0x0010     100     100     000     Old age      Offline     Never     1
199   UDMA CRC Error Count                   0x003E     200     200     000     Old age      Always      Never     0
254   Free Fall Sensor                       0x0032     001     001     000     Old age      Always      Never     63
Error Log Version: 1
Error Count: 9
Error Log:
Error 9 occured at disk power-on lifetime: 469 hours
  When the command that caused the error occurred, the device was active or idle.
  After command completion occurred, registers were:
  ER ST SC SN CL CH DH
  40 51 00 FF FF FF 0F
  Error: Uncorrectable Error
  Commands leading to the command that caused the error were:
  CR FR SC SN CL CH DH DC   Powered_Up_Time  Command/Feature_Name
  25 00 00 FF FF FF 4F 00      01:42:05.257  READ DMA EXT
  25 00 00 FF FF FF 4F 00      01:42:03.023  READ DMA EXT
  25 00 00 FF FF FF 4F 00      01:42:00.832  READ DMA EXT
  25 00 00 FF FF FF 4F 00      01:41:58.621  READ DMA EXT
  2F 00 01 10 00 00 00 00      01:41:58.620  READ LOG EXT
Error 8 occured at disk power-on lifetime: 469 hours
  When the command that caused the error occurred, the device was active or idle.
  After command completion occurred, registers were:
  ER ST SC SN CL CH DH
  40 51 00 FF FF FF 0F
  Error: Uncorrectable Error
  Commands leading to the command that caused the error were:
  CR FR SC SN CL CH DH DC   Powered_Up_Time  Command/Feature_Name
  25 00 00 FF FF FF 4F 00      01:42:03.023  READ DMA EXT
  25 00 00 FF FF FF 4F 00      01:42:00.832  READ DMA EXT
  25 00 00 FF FF FF 4F 00      01:41:58.621  READ DMA EXT
  2F 00 01 10 00 00 00 00      01:41:58.620  READ LOG EXT
  60 00 00 FF FF FF 4F 00      01:41:56.397  READ FPDMA QUEUED
Error 7 occured at disk power-on lifetime: 469 hours
  When the command that caused the error occurred, the device was active or idle.
  After command completion occurred, registers were:
  ER ST SC SN CL CH DH
  40 51 00 FF FF FF 0F
  Error: Uncorrectable Error
  Commands leading to the command that caused the error were:
  CR FR SC SN CL CH DH DC   Powered_Up_Time  Command/Feature_Name
  25 00 00 FF FF FF 4F 00      01:41:58.621  READ DMA EXT
  2F 00 01 10 00 00 00 00      01:41:58.620  READ LOG EXT
  60 00 00 FF FF FF 4F 00      01:41:56.397  READ FPDMA QUEUED
  60 00 38 68 BE 3A 40 00      01:41:56.375  READ FPDMA QUEUED
  60 00 10 08 0E 27 40 00      01:41:56.371  READ FPDMA QUEUED
Error 6 occured at disk power-on lifetime: 469 hours
  When the command that caused the error occurred, the device was active or idle.
  After command completion occurred, registers were:
  ER ST SC SN CL CH DH
  40 51 00 FF FF FF 0F
  Error: Uncorrectable Error
  Commands leading to the command that caused the error were:
  CR FR SC SN CL CH DH DC   Powered_Up_Time  Command/Feature_Name
  60 00 00 FF FF FF 4F 00      01:41:56.397  READ FPDMA QUEUED
  60 00 38 68 BE 3A 40 00      01:41:56.375  READ FPDMA QUEUED
  60 00 10 08 0E 27 40 00      01:41:56.371  READ FPDMA QUEUED
  60 00 08 FF FF FF 4F 00      01:41:56.319  READ FPDMA QUEUED
  60 00 10 E8 F1 06 40 00      01:41:56.318  READ FPDMA QUEUED
Error 5 occured at disk power-on lifetime: 469 hours
  When the command that caused the error occurred, the device was active or idle.
  After command completion occurred, registers were:
  ER ST SC SN CL CH DH
  40 51 00 FF FF FF 0F
  Error: Uncorrectable Error
  Commands leading to the command that caused the error were:
  CR FR SC SN CL CH DH DC   Powered_Up_Time  Command/Feature_Name
  25 00 00 FF FF FF 4F 00      01:41:53.979  READ DMA EXT
  25 00 00 FF FF FF 4F 00      01:41:51.778  READ DMA EXT
  25 00 00 FF FF FF 4F 00      01:41:49.575  READ DMA EXT
  25 00 00 FF FF FF 4F 00      01:41:49.550  READ DMA EXT
  25 00 00 FF FF FF 4F 00      01:41:49.477  READ DMA EXT
Self Test Log Revision: 1
Self Test Log Count: 0
Self Test Log:
No self tests logged.

Answer 1

As I'm sure you are already aware, that HDD has failed to the point it cannot find a bootable volume.
If you have a backup, no worries.
If you do not have a backup, you could try to reinstall the operating system and get the disk to a state in which it will at least mount. Then, copy whatever information remains intact to another disk. I would be inclined to replace the drive now, install the failed one in an external enclosure, and attempt to extract whatever information you need from it.