Restore from Time Machine or re-install OS X?

Mid-2011 iMac, 500GB HDD, 12GB RAM, Mavericks.

At start-up get Apple logo + three beeps. Have reseated RAM, and tested RAM through another computer - RAM is good, no problems. HDD healthy as per Disk Utlility/Repair in Recovery Mode. Won't boot to Safe Mode.

HDD was way too full (stupid me), but friend has taken 50GB+ off in Target Mode so that shouldn't be the problem any more.

So thinking the problem is the OS (maybe set off by my cramming the HDD?). I have two options: restore a Time Machine back-up (I should have one even of the morning before the crash occurred), or reinstall OSx (which, as the iMac did not come with installation discs, would mean an upgrade to Yosemite, yes?), both options through Recovery Mode.

I really don't know which option to choose at this point and would be very grateful for experienced users' thoughts. What are the relative merits/dangers of each path? Does one option stand out as being more sensible?

Many thanks

 

Hi

Thanks for taking the time to reply, I appreciate it. But, FYI, I went ahead and tried the OSx re-install and it worked. I wonder whether some script got corrupted that meant the system believed there was a hardware issue.