Your post says the computer responds to ping only from internal network. It is not clear whether there is only a single network or whether there might be more than one network on the inside. Am I correct in guessing that there is only a single inside network? The computer having an incorrect gateway would be a very possible cause of the problem. Unfortunately I do not believe that there is any debug command on the router which could show what is configured as gateway on the computer. The closest we could come would be to debug arp on the router and watch the output. If the computer consistently sends arp requests for some address that is not the router address then we can reasonably guess that the address it is arping for is the configured gateway. But it does not prove it.
HTH
Rick
HTH
Rick