1 of my 3 computers can't connect to hotspot

I have 3 computers that I need to occasionally connect to the internet through my R2D2 Droid 2. Two of those computers connect quickly and effortlessly. The third will not connect at all.

I have made sure the wireless adapter is on. I have verified the wireless key about a dozen times. I've made the password over 10 characters, using letters and numbers only. I've rebooted my laptop a few times. I've tried to Repair the connection. My computer sees the Droid in the Wireless Networks list, but simply can't/won't connect.

I'm running Windows XP on all 3 computers, with the same service packs, etc. All three connect to my wireless home network with no issues at all.

Any suggestions on how to make this third laptop (same make and model as one of the other 2 that will connect, btw. HP zd8000) connect successfully to my R2D2?

Thanks in advance.