Mike, we need you to supply more detailed information.
When you get those blue screens or other error messages, copy them exactly and post them. Let us know exactly what you are doing when you get them, and whether they are "repeatable" or appear to be happening "randomly". If it's an "illegal operation", click the details tab and give us the first two lines.
Since you installed new ram, I would suspect there is still not something right there. Provide the motherboard model number and maybe folks can tell you whether what you got is what the motherboard supports. Sometimes modules just aren't seated fully and that will cause problems.
If there is more than one module, try just one at a time. Otherwise try a ram tester such as this one:
http://www.simmtester.com/page/products/doc/download.asp
I think we may want to move you to the hardware forum, but we'll wait for further.
You should also provide a post of your current startups. Use the Startuplist application from the site below. Just unzip, run it and copy/paste the results to a reply.
http://www.lurkhere.com/~nicefiles/
If you don't have a zip program to unzip that and the system is too unstable to install one, try running
msinfo32 and click on Software Environment and Startup Programs. Then click edit>select all > edit > copy and paste the copied text to a reply.