my screen keeps going black - help!

Hi all - I have a dell inspiron 8100 notebook computer. Here is my tale of woe: Yesterday afternoon I turned on my computer and about 30 seconds into start-up the screen went black. I turned off the system and turned it on again. Again the screen went black. After about 3 more tries the computer started up properly and all was fine...until this afternoon. I used my computer earlier this morning and everything was fine. I turned it off and came back to it about 3 hours later. After I had been using it for about 10 minutes the screen went almost completely black. The computer was still on, but the monitor was dark. I turned off the computer and restarted it. The screen went black after about 3 minutes. The same thing happened about 4 more times before I decided to call dell for support. The dell representative I spoke with had me take out the battery, unplug the power source, and hold down the power button for 30 seconds. I then restarted my computer and the screen went dark after 3 minutes. He then had me reinsert the battery and restart the computer. Once again the screen went black after 3 minutes. The representative said it sounded like I had a loose connection; however he couldn't tell me how to fix it since his system was down. He said he'd call back again this time tomorrow - but I'd like to fix this asap. So I'm now writing you for help from my husband's computer. Help me please...what can I do to fix my computer? Thanks! - Margaret