PAY CLOSE ATTENTION TO THE PART NUMBERS, like on the bottom link "C47NF" and "NXH8C" from Ebay.
Look at the old board that failed and make sure to find a replacement with the exact same numbers.
Here are a couple choices:http://compare.ebay.com/like/350538052937?var=lv<yp=AllFixedPriceItemTypes&var=sbar&_lwgsi=y&cbt=yhttp://www.upperedgetech.com/dell-xps-l502x-motherboard-c47nf-geforce-gt-525m-1gb-same-day-shipping/
Looking at the specs in yours, a replacement with equal specs is at least 1,000.
I've had the best success with HP and Sony VAIO, never had much luck with Dell.
I hope that Ebay Seller accepts the return, and you find a working replacement.