It sounds as if you aren't receiving position packets from other cars. This is likely caused by either a router or a software firewall blocking the UDP traffic. You need to find a way to allow LFS' UDP traffic to pass to and from you. You can try clicking the UDP/TCP button in the in-game connection list, but I doubt that will do anything.
If you need to open specific ports for LFS, they are usually 63392 and 29339 (both TCP and UDP).