You probably don't have bad ram after all, I thought your system was only reporting 3GB, please be clearer in the beginning (the edit helped). It wouldn't hurt to run MemTest86 anyway, but make sure you run it when you're out at work or something, a proper test takes hours to complete.
If you have a Windows 7 installation DVD that's an upgrade or retail install, you can format and change to 64-bit. Make sure you backup your files first though, as a format will erase all data.
However, if your computer came with Windows 7 pre-installed via the manufacturer or you have an OEM disc then you'll need to purchase a new disc that is 64-bit. You can either get a 64-bit OEM disc, an upgrade disc or a retail disc. The last two come w/ both x86 & x64 as choices.
Anyone else feel like repeating me?