The router will only slow down the transmissions that go through it.
My home LAN has 1GB nics in all the PCs except one, with a 1GB switch, internally, everything happens at 1GB. The one PC with a 10/100 is the gateway PC and it only has a 10/100 as the Internet connection happens at under 100 MB so it doesn't need the 1 GB.
If your LAN is set up with three switches (s1, s2, s3), 1 router (rA), and 15 pcs (5 off each switch as c1 to c15 - c1 to c5 off sw1, c6 to c10 off s2, c11 to c15 off sw3); it can be set up a number of ways.
Lets assume all switches connect to the router and you can't go between switches except through the router. Each group of PCs off each switch will talk 1GB to each other, but transmission from pc 1 to pc 14 going via s1 to rA to s3 will be reduced to 100MB for having to go through the router.
However, if you have your system set up to allow s1 to up link to s2 and s3 so the switches can talk to each other directly, and the router sits between them and the Internet, then the whole internal network will be 1GB and only drop down when going outside.
How you set things up will depend upon the physical and logical network you're dealing with.
The common trick is to have the router in the center and the switches all off it, and the pcs off the switches, then you need to change the router to 1 GB if you want 1GB network, also make sure the cable can handle 1GB.
Most switches today easily handle up linking between switches on the same physical network, easier if they're also the same logical network. Routers are only needed to link between different logical networks. Mostly used as gateway cops now days.
edited to add - I've seen a small business network with an adsl modem router that had 10/100 ethernet ports. The internal network was 1 GB as they had a switch for each of the three open plan office areas, and these all connected to a 4 port switch that was also connected to the router. All internal activity stayed within the switches and didn't touch the router, but all Internet traffic went through the switches to the router and out to the world. you may want to consider such a system as well, another switch is cheaper than another router.
