I've seen this happen a lot, hell, I've done it myself, you break off a component on the motherboard, then have no idea what it is, to find a replacement.
I just bought a dead X360 motherboard, I've pretty much given up on fixing it, it's pretty far gone (fell off a balcony), so here's what I'm gonna do:
For anybody that has broken off a component on a 360 mobo, give the part number on the board and I will remove the part from this parts board, measure the part, and reply back with the value so you can find a proper replacement. I may offer some of the larger components for sale (connectors, switches, coils, capacitors, larger IC's, etc).
I'll keep you updated, this is definitely going to be my parts board unless by some miracle I can fix it (Best I got out of it was to boot then freeze immediately in the little startup animation).
Later
-Tim