I normally wouldn't recommend it because laptops are so confusingly built and they usually require specialty knowledge, but if you've got someone who knows what they're doing, go for it. Just make sure to by the same model of motherboard, cause those things almost never port.
Shrew is quite correct, and then finding one that fits properly...Quite the hassle. IS THAT THE MOTEHRBOARD? No, that's the sound card. Huh. Whooooops.
Right now I should probably differentiate between proprietary and generic motherboards. Generic motherboards are fit to a certain standard (usually ATX) and is compatible with any other parts that fit that standard. Proprietary motherboards are a bit of a problem, because they're manufactured for one specific set of products, and rarely work with any others.
Dell Inspirons, like most laptops, are proprietary. To my knowledge, I don't even think an ATX-like standard exists for laptops. If you're trying to replace the motherboard on a laptop, don't bother. But if you getting a new laptop, do take your RAM and hard drive out of the old one, because those two parts are the only two that usually transfer well from laptop to laptop. Plus, if it's your motherboard that failed and not your hard drive, then all your data should still be alive and well on your hard drive.
If you are looking for a desktop motherboard, that is a whole other deal. Almost all desktops are now manufactured to the ATX standard (or one of ATX's variants), and then you have to pay attention to what kind of RAM, socket type, and so on you're getting.
And for what it's worth, you may want to boot the other person's computer up with a Linux LiveCD when you try to copy the data off, just to help prevent any infections from spreading from your hard drive to theirs.
I read two things - power surge may have fried the video card or memory modules. How many beeps does it make? Sometimes (like with IBM thinkpads) the beeps are a code for what the problem is.