Like I said earlier, some routers will send out pings to determine what's talking on the network. Even if it doesn't find anything, it'll keep going every so often to try and locate new machines. Our old router used to do this, and it would show up in ZoneAlarm logs on my dad's PC every day.
Since you're running NAT services on the router, a ping request from the outside would be answered (or dropped, if it has its own firewall) by your router, not forwarded along to PCs on the inside. That would mean pings on the inside are coming from the inside. Are you able to check what IP address those pings are coming from?
UserAgent: Mozilla/5.0 (Windows; U; Windows NT 6.1 x64; en-US; rv:1.9.3a1pre) Gecko/20091116 Minefield/3.7a1pre
Laptop: HP Compaq nx6325 - Turion 64 X2 @ 2GHz, 2GB DDR2, 100GB HD, ATI Radeon X300, 15" LCD, Seven Pro
Handheld: Palm Treo 650 - Intel PXA270 @ 312MHz, 10MB RAM, 32MB flash, 2.7" LCD, Palm OS 5.4