laptop?

If it start but the screen is blank, it's not a battery problem. DON'T EVER let your battery totaly drained for any prolonged period, it WILL KILL it. Less than 5 days is acceptable, longer greatly increase the risk.

A few possibilities:
The operating system installation may be corrupted, most likely some missing files on C:\. In this case, you'll see the POST screen, but the screen then goes black, with mabe a blinking underscore in the top left, and nothing else appens.
It's quite possible to delete some of those critical files while the OS is up and running (I've done it...). You'll only get the problem the next time you boot the computer.
If that's the case, you need a live CD to backup your data to some external drive, or other medium, then try a repair or reinstall the operating system.

The hard drive may bad. In this case, you'll probably get some error message about non-OS or non-system drive.
You need to reinstall the operating system on a NEW drive.
Once it's done, reconnect the old drive as the D:\ drive and attempt to recover your files.

If you get a message about no media, unrecognised media or some more or less cryptic error message, then the hard drive is dead and need to be replaced. All data it contained are to be assumed LOST.

The screen may be disconnected. You need to open the case and reconnect the screen connector. In this case, you won't even see the POST screen.

The screen may be deffective. You need to replace it. NO POST screen visible at all.

(the POST screen is the pagefull of text you can see first as you power up the computer)

Electro
April 2012