Your school network is probably dynamically assigning you an IP addie to get on their network, but at home you have no DHCP server. Your computer will just default to a bogus IP 169.xxx.xxx.xxx on 255.255.0.0.
Do you have netBEUI installed on both your computers? Click on add from your network screen and add this protocol to both if not. Then from the TCPIP settings for your network card unbind TCPIP from File and Print sharing. That may fix your problem right away. If not, Start, Run, winipcfg.exe on both computers and see if the subnets match or if you have conflicting IP addies.