Start with boot key combo Command-Option-P-R
https://support.apple.com/en-us/HT201255
Then boot from OS X install disk. Run disk utility disk first aid.
If it shuts down while in the middle of this it may be a thermal issue. Is the fan clean?
How much room is left on the hard drive? Replace hard drive?
Are you installing the RAM symmetrically? Maintaining parity? If there are four slots of RAM, then install on 1 and 3. Equal amounts in both slots. There will probably be a very little 1 next to the first slot on the logic board.
Reseat all cables connecting your hard drives.
Make sure no dust has accumulated on the internal components. Blow off with compressed air if dusty.