Use a CAT 5 cable to connect the modem to the "Server" fit another Network card and run it off that as there are numerous issues with a USB connection. Just a word of warning here however if they have a Gigabit LAN connection on the server you'll have to use the same type of plug in card as a normal "cheap" one will prevent the system from working. Currently there is no way around this problem as Windows will not start in any mode so you can configure the cards separately.
Under ideal conditions the LAN speed should have no effect on the modem connection but again there are numerous problems with a USB connection.
I've personally fitted a similar type of modem to both Gigabit and 10/100 T Base LAM's without a problem as the speed of the modem is not affected by the speed of the network connection it is just how fast the Modem can feed the data to the LAN or transfer it up the modem will not accept speeds greater than it can handle so it is a "Network" problem that you are looking at here.
What type of M'Board is in the Internet gateway unit? If it is one of the older ones with USB 1 on-board it will appear to be slow over a network as the modem can download data to the USB port faster than the USB port can accept it. Have you tried disconnecting the rest of the computers and seeing if you have a decent Internet Connection Speed at the Gateway?
Lets know how you get on.
Col