Boot and run the Dell diagnostics to rule out a simpler, cheaper possibility - that the hard drive is failing.

If it's constantly a no post issue like you explained, then it could be the motherboard.

 

I'd go ahead and remove all other devices that you can and try turning it on see if it'll post properly then.  Remove battery, harddrive, optical drive, wireless, modem, and try turning it on.  If no luck, you could try removing all memory ot make sure you get a memory beep code.  Assuming you do, try putting just one stick in, and try all configurations with those two sticks of memory, see if there's any patterns.

 

If you're not getting a "no bootable device message" with any memory configuration, but your not getting memory error codes, i'd say it's likely the motherboard (assuming your display is working).

If your having the 5150 shuts down on boot or when touched problem, this post I've been putting everywhere may help.

--------------------
I recently had the "5150 shuts down when bumped" problem and after some searching around I found some instructions here:
http://www.hardwareanalysis.com/content/topic/43678/

I followed the advice, with the exception that I didn't pull my laptop apart, I did it all just by removing the C panel and the wireless card.

Its been working perfectly for a couple of days since and I updated the post above with my own steps. It took me 10 minutes from removing the C panel to putting it back on again, I've been carting it around while it's running and I can use the palmrest again without fear, it has not shut down once since I performed the repair.

Hopefull that will be of some assistance to people. Its certainly cheaper then paying Dell for a new motherboard.

rgds

Franki