Presario V5000 The Computer no longer turns on. When I press the power button, the "lightning bolt" icon on the front of the laptop blinks a few times and that's all that happens. Any suggestions?

Depending on your Bios Version I think later then V44 fixed a bug that would cause your computer no to start if the battery was dead with the V5000. Remove the battery and try booting from just AC power.
I have also had the same issue when my bios battery is loose or dead. The battery can be accessed from the memory area. Once you open it on the left should be memory and on the right will be the wifi card. You don't need to unplug the cables just remove the wifi card and examine the battery. The battery is held by a very very flimsy piece of platic and really easy to break. The best thing I have found is using a little piece of cardboard from a box or something and using it to keep the battery tight, just dont go shaking the laptop alot and it will hold it. It might also be possible your bios battery is dead.
From what I say I would hit power it would power for about 3 seconds the power light would flash then turn off.

Battery must be busted...

Have you tried replacing it?
Also, try pressing and holding the power button.