[?]I have a fujitsu siemens c771 monitor and I use 3dfx banshee.
I can not get full screen display size under 800*600. In addition,
the refresh rate can only be set 65Hz, if I set it higher than it, the display size will get much smaller and dark. If I change to 1024*768 mode, I got the same problem. The display size is too small and dark. Before I use this new monitor, I use a compaq 15 inch monitor, there is no problem at all. Is there any problem with the monitor and video card?

The C771 is a 17 inch monitor and your "old" monitor a 15 inch.
Try to choose the correct inf. for the Fujitsu monitor or to choose "plug and play monitor".

edit : what's the exact reference for your monitor ? on Fujitsu' Site, you find several C771's.