Thanks for posting up your system specs.
I think the fundamental problem with your system is that you only have 1GB of RAM (and its very slow RAM too) - for Windows 7 32bit the minimum recommeded is 2GB, and you are running Windows 7 64 bit. Can I hazard a guess that your system is generally very sluggish?
Lets have a look at how Windows rates your system performance. Can you please follow these Steps:
2. In the search box, type Windows Experience
3. Select the option Check Windows Experience
4. In the panel that opens, please select Re-run the assesment
, as shown below
5. When it is complete, take a screen capture of this panel and post it here in your next reply.
I think the best thing you could do is add more, and faster RAM to your system. It will make it snappier and perhaps avoid some of the shutdown issues you were having. Prices of RAM have dropped dramatically since 2007 so I think this could be the easiest and cheapest way to treat your system to a makeover.
Regarding the BIOS, before you update that, read up a bit on what the updates may deliver. We have seen many instances here where an incorrect flshing/update of the BIOS completely wrecks a system to the point of no recovery. Research it carefully, and be cautious.
Let us know if you need help selecting RAM if you don't feel confident with that, and we can do that for you.