My mac is not starting up

Question

Yesterday, my Mac froze. I could move my mouse around but that was it. So I turned it off and back on and a white screen came up. After that a flashing folder with a question mark on it showed up and that was it. So I tried again and the same thing came up. I looked up what I should do and I read somewhere that it might work if I keep the option button pressed after turning it on. I did that and it started up and worked for like 5-10 minutes but it froze again. So I tried that again and now my mouse just shows up on the blank white screen whenever I keep the option button pressed after turning it on. If I just turn it on without pressing anything, the flashing question mark folder just shows up. I'm reluctant to send my Mac to the Apple Store because whenever I start up my Mac, Skype log in shows up and the username is a very personal one that I don't want anyone to see (but I understand that I will probably have to send it in). What should I do?
(Mac info: I don't remember the operating system. I got my Mac in the middle of 2010.)

Answer 1

Question (?) Mark, Blinking Folder, or Gray Screen at Startup
These are related but not identical issues. Their causes are outlined in Intel-based Mac- Startup sequence and error codes, symbols. Solutions may be found in:
A flashing question mark appears when you start your Mac
Mac OS X- Gray screen appears during startup
In most cases the problems may be caused by one or more of these:
a. Problem with the computer's PRAM - See Resetting your Mac's PRAM and NVRAM.
b. Boot drive's directory has been corrupted - Repair with Disk Utility.
c. Critical system files are damaged or deleted - Reinstall OS X.
d. The disk drive is physically non-functional - Replace the hard drive.
Note that the information I have provided is what Apple recommends, If other users suggest different solutions than found here, then be sure what they recommend does not impact on your warranty, if any, or ability to get continuing Apple service.
Please don't start removing drives or changing cables unless you know what you are doing and have exhausted other non-invasive alternatives outlined here. If you perform any work yourself that is unapproved by Apple, then you will void any warranty you may have and lose all further Apple Support.
Repair the Hard Drive and Permissions
Boot from your Snow Leopard Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list.  In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive.  If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer.
If DU reports errors it cannot fix, then you will need Disk Warrior and/or Tech Tool Pro to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.
The main difference if you are using Lion or Mountain Lion is that you must first boot from the Recovery HD. Simply boot from the Recovery HD to perform the above.
Reinstall Snow Leopard Without Erasing The drive
1. Repair the Hard Drive and Permissions
Boot from your Snow Leopard Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Utilities menu. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list.  In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive.  If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer.
If DU reports errors it cannot fix, then you will need Disk Warrior and/or Tech Tool Pro to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.
2. Reinstall Snow Leopard
If the drive is OK then quit DU and return to the installer.  Proceed with reinstalling OS X.  Note that the Snow Leopard installer will not erase your drive or disturb your files.  After installing a fresh copy of OS X the installer will move your Home folder, third-party applications, support items, and network preferences into the newly installed system.
Download and install Mac OS X 10.6.8 Update Combo v1.1.
Reinstalling Lion/Mountain Lion Without Erasing The Drive
Boot to the Recovery HD: Restart the computer and after the chime press and hold down the COMMAND and R keys until the menu screen appears. Alternatively, restart the computer and after the chime press and hold down the OPTION key until the boot manager screen appears. Select the Recovery HD and click on the downward pointing arrow button.
Repair the Hard Drive and Permissions: Upon startup select Disk Utility from the main menu. Repair the Hard Drive and Permissions as follows.
When the recovery menu appears select Disk Utility. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list.  In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive.  If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the main menu.
Reinstall Lion/Mountain Lion: Select Reinstall Lion/Mountain Lion and click on the Continue button.
Note: You will need an active Internet connection. I suggest using Ethernet if possible because it is three times faster than wireless.