You also might have a super super old and crappy cable that can't do it itself. If any link in the chain isn't giga, then it won't be. Though really if you're talking about it telling you that in network settings then it's either the cable or the first switch/router it runs into.
also the ISP and the router they give you...may have an automated speed control, if there are more then one pc attached to it..even through a switch... it can adapt speeds to loads...the pc with the highest demands, will be alloted the most speed. and then the others will be cut down.. I hate this and wish i could bypass it...as several computers play games and HD video similtaneously...and only one pc is given 100mbs full duplex...
There are a few incorrect statements here. The link speed is only determined by the device it's connecting to. If your NIC is 1G and your switch or router that it's physically connected to will do 1G, you will be 1G. If there's a downstream link somewhere else that's 100Mb or even 10Mb, you'll be limited to your throughput, but you're still connected at a gig.
The caviat to that is some NICs don't handle 1G very well. Don't hard code 1G NICs. Set everything to auto and you should be good. Your issues could be a NIC issue as opposed to a cable issue. I would be willing to bet that's the case.
Yes, cat5 will handle 1g easily, but as you get longer distances, you may see issues. Within a house/apartment/flat/whatever, any cat5 cable or better should suffice.