That would need some kind of SNMP logging or packet sniffing. I don't think XP has built in SNMP logging capabilities and packet sniffing is hard and messy. Maybe there's some third party software out there, but I haven't seen any.
Possibly who is using your shared files and/or surfing through your ICS (or other router software) but nothing else. What goes on on the LAN is unknown by your computer. It only cares about packets directed to itself.