Remove the battery and try running it with just the adapter. If it works, the battery is dead. You can just leave it like that and save the $100 for a new battery or put it towards a new computer. With $300-400 laptops available now, it would be silly to waste money on the old one.
My dell Inspiron 4000 Laptop has died. The first sign was a reluctance to start, either on battery or mains power. Many presses of the start button were needed. Then it would not start at all so I put it on one side. A few days later it started, but there was no screen display and then it just powered down and died. Occasionally it would start but there was never any screen display and after about 10-15 seconds it powered down and died. The battery is fine and fully charged. Is there a relatively inexpensive remedy for this tired old laptop or should I just bin it?