Connection switches to Local Only?

I connect to the internet by a 56k dial-up connection. I've never had this
problem with XP or 2000, but in vista I think they changed how you connect to
the internet. Maybe I'm wrong about that, but for some reason after
connecting to the internet (usually after starting a full screen application,
like a game, but sometimes in IE too) my connection switches from local and
internet to local only? What I mean is if you hover over the network icon in
your tray on the bottom right it says:

Currently connected to:
"The name I gave the connection"
Access: Local and Internet

Then it switches to:

Currently connected to:
"The name I gave the connection"
Access: Local Only

Is there anything I did or didn't do that switches it? why does it switch to
local only? The reason I ask is when it switched to Local Only I am unable
to connect to any websites unless I have them available in "Work Offline"
mode. This also disconnects me from any online programs that I might be on
at the time. Very frustrating to be in the middle of something and get
disconnected and have to reconnect to the internet 20x an hour

I went into the Network and Sharing Center, and at the top it shows the "map"
of your connection. It shows me my computer's name then a line over to the
name I gave the connection, then in the line from there to "Internet" is X'd
out and Internet is grey. Maybe that might help explain what I mean. When I
first connect, for about 5 seconds it is shows "Limited" then it switches to
Local and Internet, then later it switches to Local only.