06 May 2010 at 15:13 - 3
From the markings on the board (in the picture), it looks as though it's a small surface mount capacitor. It would be possible to solder one back on, but the original one (if you still have it) may be damaged. It would be very difficult and time consuming to figure out what size (capacitance-wise) capacitor to replace it with, unless the value is marked on it. It would also be very difficult to find a retailer where you could buy a new one, but you might be able to salvage one from some old piece of dead electronics.
Overall, repairing it would involve the delicate use of the proper soldering equipment, knowledge of the markings on the capacitor (and how much variance you can allow) and finding a replacement part.
Given all that, your best bet is to buy a new (or used) network adapter and install it. Make sure the new or used adapter is at least 100MHz. (Could be marked as 10/100, 10/100/1GHz, etc.) You may need to get into the computer's BIOS to disable the on-board adapter in order for the plug-in to work.