Is the damage to the motherboard is likely caused by the old battery. Look at board repair or replacement found with a search like http://www.google.com/search?&q=dell+laptop+motherboard+repair&
Here's my issue. My laptop will power on (the indicator lights come on) and I see a brief flash of the initial Dell screen - but then nothing happens. The screen stays blank and nothing else happens. I had been getting messages that my battery was 'reaching the end of its normal life' and needed to be replaced. Since it stopped working, I replaced the battery but that doesn't help.
Any suggestions on how to troubleshoot (and hopefully fix)? Thanks!