This is my 3 cents worth (inflation and all that
) but I'm thinking DirectX! Please follow this. You changed your video card. One of the important and oft-complained issues with FL is video related problems usually traced to DirectX. Part of the DirectX package is DirectPlay which is needed for MP. If it was ports being blocked or redirected, some other program would have to be making use of them. Plus it would have to be low level and for the system, i.e. low level in that you don't "see" a program running (usually running as a service or lower still) and loaded by the system at start up. In other words it would be hard to find. Try reinstalling DirectX v9.0b, the latest.
Other games may work with earlier versions of DirectX or those games may not be using DirectPlay (hence that part of DirectX). Might explain why they work and FL doesn't.
I had a similar problem but it was due to my software firewall, Zonealarm. It wasn't "trained" to allow FL to work and hence blocked all the ports initiated by FL in BOTH directions.
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Earendil
SysAdmin of Boston Freelancer server