jeregrl welcome to the forum.
I have a good idea what may be causing the problem. I have a feeling that what is causing the problem is the bloat/crapware that HP (and the rest of them (Dell, Acer, etc) like to install) in the form of HP's connection software, that overrides Vista's default connection settings. If I am right then if you can find it (or them, last Acer I worked on there was at least two different variations of the same thing) and disable it, things should be normal.
To disable it open msconfig (click on Start and type msconfig in the search box) and click on the Startup tab and see if you can find anything relating to HP and internet connections. There may also be a service (same as above only this time type serv and then select Services from the list) and see if there is anything similar (leave and of the Windows services alone)
How does your opinionated tirade help cure the OP's problem? What specific advice do you offer? It's people like you who have less knowledgeable users doing more harm than good to their systems by listening to "generic rubbish"
Offer some concrete advice or simply say you don't know, and point them towards someone who does, like HP's Tech Support, but don't tell them to remove stuff without telling them what that "bloat/crapware" is.
P.S. Be nice if someone more familiar with the HP specific software could weigh in here and point jeregrl to the correct items in msconfig and Services to disable.
Is the best advice given thus far.
To the OP,
Are you wireless? If so, do you get a constant connection? Might it be your connection settings?
You can run a diagnostic check on your internet connection by going to:
"Control Panel",
"Network and Sharing Center", under your network click,
"View Status", when the "Local Area Connection Status" box opens click,
"Diagnose" and see what it says, then go from there.
Also, go into your
"Control Panel",
"Windows Firewall",
"Change settings",
Click "Exceptions" tab and check to see if your game is listed, if it is, make sure the check box next to the game is checked. This tells your firewall the game is good to run. You can also check to see what other items are blocked, but be careful.
Let us know.