Diagnosing problems like this is always a process of elimination. A bad (or even missing or disconnected) antenna would only cause range problems (e.g. it should still work while sitting within a few feet of the access point), so if the adapter is "dead" you can pretty much rule that out.
Besides the card and motherboard, there is also software involved (OS and drivers). If you have the latest drivers properly installed and configured and yet the card does not show up in the device manager, then that could be a bad card (most likely), but it could also still be a corrupted OS or a bad motherboard. If the card is recognized but just doesn't seem to work, then that would most likely be just the card or software.
To positively verify whether the card is defective, the standard procedure would be to replace it with a known-good spare. If the spare works, then the original card is defective. If not, then the problem lies in the motherboard or software. A corollary to this would be to install the original card in a known-good system (one with an existing card that works). For example, if the original card works in the known-good system, then you have verified that the original card is good.
If the card is good then that leaves software or the motherboard as the remaining suspects. To rule out software I would temporarily install a new (clean) OS and drivers. Note that you don't have to blow away the existing installation, as this could be accomplished via booting from a liveCD, USB connected HDD, or a temporarily installed internal HDD.
If you have ruled out everything but the motherboard, then that would leave the worst-case scenario, a motherboard with a defective internal card socket. In that case you can either replace the board (expensive!), or simply ignore the defective socket and install an alternative (i.e. PC-Card/CardBus, ExpressCard or USB) card instead.
Let me know what the problem and solution turns out to be, Scott.