Please post your system specs and the blue screen error messages in full, inclusing Stop codes.
Run memtest on one stick of RAM at a time to test for any errors.
Direct link to pre-compiled bootable ISO (click the link to download the zipped ISO file)
http://www.memtest.org/download/1.70...+-1.70.iso.zip
Unzip the file and burn the ISO to CD (as an image, not as data) to create a bootable CD. Reboot and go into the BIOS. Change the boot order to 'CD first', save settings, insert the CD and reboot. This will start the program. Run for one RAM stick at a time (very important) for at least 10 passes each and post back with the results.
It's not a good idea to run the computer with the case open for too long. Dust gathers around the slots, heatsink and fans, causing overheating. Where was the broken fan positioned?
Replace the faulty fans and put the side panel back on. Proper airflow will help with the temperatures.