Try removing the added memory. A bad memory stick can cause all sorts of problems.
To troubleshoot this, return the machine to an "as stock as possible" configuration before you upgraded -- put back in the old hard drive, take out the added memory, etc. Then, one by one, add them back: add the hard drive and use the computer for a day or so and see if it's stable. Then, add ONE new memory stick and do the same... if all's well, add another, and so on and so forth. This will help you to narrow down the piece of hardware (if it IS hardware) that's causing the problems.