I have to ask, what do you mean by not connecting at 1 Gbps?
Are you saying that the ethernet card is reporting only a 100 Mbps connection, or are you expecting 1 Gbps speeds and are not getting anywhere close?
If the ethernet is connecting to the switch at 100 Mbps, first off, to state the obvious, make sure the card is in fact a gig-ethernet card. After that, try a different cable, followed by making sure latest driver is installed, and finally make sure the card's properties are set for max speed. If Auto-negotiate is not enabled, try that. Last option would be instead of auto-negotiate, set the card to run at 1.0 Gbps full duplex and see if that works.
As far as switching to cat6, 5 or 5e should work fine.. FWIW my main PC here connects @ 1 Gbps just fine through about 125' of cat5 I ran from the basement to my 3rd floor sometime back in 2004/5