After updating to yosemite, start up and recovery mode freeze

Question

I recently got a 2010 Macbook Pro off of ebay and it was on 10.6 so I decided to update to 10.10. After updating it told me to restart so I did. Well after restarting the spinning wheel froze so I restarted it again. It does the same thing. I googled around to see if anyone had the same problem as me, plenty of people did, they said that they found the recovery partition and the Mac started working again, so I tried finding the recovery partition by pressing shift, option, and r (or something like that) and it turns out I don't have one. Then I tried Internet Recovery and that was a bust too, so now in stuck with a $700 paperweight. I'll post the sspecs on my Macbook below -
Brand: Apple
Processor Type: Intel Core 2 Duo
Product Family: MacBook Pro
Processor Speed: 2.40 GHz
Screen Size: 13.3"
Operating System: Mac OS X 10.10
Memory: 4 GB
Release Date: April, 2010
Hard Drive Capacity: 1 TB
Model Number: A1278
Serial Number: W8*****ATP
Model ID: MacBookPro7,1
Charging: 60 Watt MagSafe 1
<Personal Information Edited by Host>

Answer 1

Peter
Do you have a back up? What version of iPhoto do you have? Assuming 09 or later:
Option 1
Back Up and try rebuild the library: hold down the command and option (or alt) keys while launching iPhoto. Use the resulting dialogue to rebuild. Choose to Repair Database. If that doesn't help, then try again, this time using Rebuild Database.
If that fails:
Option 2
Download iPhoto Library Manager and use its rebuild function. (In early versions of Library Manager it's the File -> Rebuild command. In later versions it's under the Library menu.)
This will create an entirely new library. It will then copy (or try to) your photos and all the associated metadata and versions to this new Library, and arrange it as close as it can to what you had in the damaged Library. It does this based on information it finds in the iPhoto sharing mechanism - but that means that things not shared won't be there, so no slideshows, books or calendars, for instance - but it should get all your events, albums and keywords, faces and places back.
Because this process creates an entirely new library and leaves your old one untouched, it is non-destructive, and if you're not happy with the results you can simply return to your old one.  
Regards
TD