Vostro 1500 won't boot without external power

I am working on a Vostro 1510 that has a very strange boot problem. Have read many threads with similar issues but none seem to fit my symtoms exactly.

Problem: When booting with good battery, boot fails before post with flashing numlock light. Have tried two known good batteries. If the system has AC adapter plugged in it boots perfectly every time. If, after booting with AC and I remove AC power from machine, I can restart system without problem. However, if I shutdown completely it will not boot again using the power button.

An exception to this is that if the system has been running for sometime and is "warmed up" it will boot with battery only for a few minutes until it has had time to cool down.

Adding to the confusion is that once I get the flashing numlock light I must remove the battery to do a complete power down before connecting AC adapter again.

I have used known good memory sticks and removed HDD and DVD drives. Same symptoms when booting from USB. The bios battery has been replaced and the Bios is at A15 which is the current version according to Dell.

Process of elimination tells me this is a motherboard problem.

Should I shell out the bucks or am I missing something? Thanks!

EDIT:
Problem solved. In case someone else has this problem, here is what I did. I used a heat gun to preheat areas of the motherboard and found that all I had to do to get it to boot with battery power only was to heat up the 9 battery connection pins. (used a heat gun set to 400 f for about a minute so as not to damage plastic parts) After going thru a successful boot - cool down - boot fail - pre heat - successful boot process 3 times, I was convinced this was the problem.

Then I took a soldering iron with a large tip set to 400 degrees and heated two pins at a time until the problem was isolated to just two pins. Then I raised the temp to 600 degrees f and heated those two pins for about a minute in order to reflow solder connections.

Working perfectly now...