Cannot connect to wireless network

I am having problems with the wireless adapter provided with my PC. It can see my wireless router (a Netgear DG824M) and the signal strength is excellent, but it is unable to connect. I either get Limited connection or no connection at all. (It shows "Identifying..." in the Network map.)

From the manual, the wireless adapter is a Asus WL-138GE or WL-138G V2. Windows recognised it as a Broadcom adapter, so I downloaded a Vista 64 bit driver from Asus and installed that. The adapter is now recognised as a Asus 802.11 adapter, but this has not made any difference to being able to connect. The driver provided by Asus does seem to be quite old (2006 I think), and still references Broadcom. There is an Asus utility CD provided by the PC, but this doesn't seem to run on Vista 64.
I have had the connection work pefectly 3 times, but then, the next time I reboot, without changing anything, it stops working. For example, yesterday I turned off Windows Firewall, rebooted, and it worked. The next I booted, still with the firewall disabled, it didn't work.

It seems that the wireless card is unable to get an IP address from the router, as its address is often rubbish, instead of something in the 192.168.0.0 range that I am expecting. I have a laptop, running the equivalent 32 bit version of Vista, and this has no problems connecting. As far as I can tell (I'm not a networking expert), there are no differences between the network set up on the 2 computers. What I'm trying to achieve is to have them both talking the router and each other, so I can share folders and printer, and synchronise the two using Microsoft's SyncToy.

As the PC is new, I've also sent this to the supplier's technical support, and I will problaby post on the Asus forums as well (I had a quick look there, but haven't found a solution).

Thanks,
Oliver