First take your battery out its probably the culprit. Try your computer with another adapter if you can without the battery if it works you've got the answer. Get a new battery. I've come accross similar problems and the battery was the cause.
Second, to save your data take the HDD out, they normally just pull out on Dells, take it out of the chassis so you just have the HDD without the Dell connectors. You will have to buy an adapter that converts you laptop IDE into a full size IDE or you can get IDE to USB adapters, (just make sure its a laptop size IDE connector though).
Now you can either plug your laptop HDD into a pc's IDE socket or into any computers USB and you can get all your files off.
The Laptop IDE to PC ide adapters are cheap only about £10-£15 the usb adapters are about £20-£30.:cool: