Desktop boot problems are difficult at best. Laptop boots are further complicated by power issues.
First things first. I will assume you have an external monitor jack on the laptop somewhere. Hook this up to an external monitor and this will help eliminate the display. If the problem is the same, the display is probably (note: probably) okay.
Second, if you have an operating system disk, attempt to boot from the disk. If you can do this, re-install your OS. At this point, consider buying a new system and selling yours for parts.
Third, if you can find someone with the same model or a spare battery, replace the battery (don't buy one unless you can return it since we don't know if this is the problem)
Fourth, if you can find someone with a 2.5" hard drive with the same interface as yours (probably IDE at that age), swap the hard drive and see how that goes.
The worst (even though it's probably time) is that some chip (maybe even the CPU) has died and you may require a new motherboard.
