program disconnnects after log in

We are having some issues with our computer running sl.( Our other computer, which is a laptop, not a desktop, is running fine.)
We are running an hp pavilion elite, with 8 gigs ram, ati radeon hd 3650 graphics card with windows vista 64 bit.
We are having issues staying connected to sl, it logs on fine, but once the graphics come up for the computer nothing will rezz, we see the basic form for our avatar at times, no other prims around us just water, and then we crash, there are several people that use this computer and all are having issues.
But we do have a wireless connection, the best you can get and always at 56. Both computers can run at the same time with sl running, the pc just crashes.
So I am wondering if anyone has any suggestions why our computer is not running sl very well, and how to remedy the situation.
Thank you very much.

we are still having issues, and have tried everything, also i noticed when i tried to log into sl, my internet browser also loses connection, and i am forced from 56, to 46 for connection on my modem, this is driving me absolultely crazy, i can sometimes stay online for 20-30 minutes and then sl crashes

Hmm have you tried uninstalling AND deleting all SL-related folders from Documents and Settings before reinstalling?