OS X Yosemite :: IMac Shutting Down Unexpectedly

I have a late-2009 27" iMac i7 with 8gb Ram and a 1TB HD. I updated my OS to Yosemite soon after it came out. Now, I admit I don't use the computer that often, so it took a while to notice the issues but, we first realized there was a problem in early November when my husband could not download a game (presumably because of the wi-if connectivity issues supposedly fixed in the latest update). It was around a week after he finally was able to download tthe game, that he was playing it and the computer would just shut down out of nowhere. No warning, just shut down and restart with the "your computer shut down unexpectedly" screen.

Now, because it happened so many times, I started to get worried about all of my photos and music that is stored on thIs computer, so I went to do a back-up on my time capsule. This was when I noticed my computer had at some point been renamed (not by any human) to "my Computer (3)" when prior to yosemite (as far as I can tell) it was named "my computer". Also at this point I could not for the life of me get the time capsule to back up the computer as it was looking for "my computer" and all that was available was "my computer (3)". This is when it had been working flawlessly for years. I ultimately had to wipe the TC completely, reformat it and start a back up from scratch. It was for the short period of time that the time capsule was not connected to the computer that we noticed it was no longer shutting down unexpectedly. however, one the TC was reconnected and doing a back up, anything extra that you would be doing (with the exception of web surfing) caused the computer to crash.

So, simple fix, right? Turn off the auto back ups while and try to remember to turn them on every so often. fine , dandy, whatever. However, I have done the latest yosemite update and the wi-if still does not seem to be staying connected, disconnecting every few minutes. Now I'm seemingly having more issues with a game that is well within the limits for my computer and the game will not start.

Info:
iMac (27-inch Late 2009), OS X Mountain Lion (10.8.3)