First: ASR == Automatic Server Recovery. This is HP's heartbeat/watchdog timer that helps the system recover from OS or hardware-caused lockups. There typically won't be an OS-level logs. You'd need to view the server's Integrated Management Log (IML). You can see that from the ILO.
You're probably due for a system board replacement, given the age of the server. I suggest this based on having deployed a lot of those systems in 2004 and early 2005.
The HP ProLiant G4p was a stop-gap and small improvement on the G4 systems. The system boards of the G3 and G4 server had a predictable failure pattern.
In your case, the ILO shouldn't report much, other than the system watchdog-initiated reboot, but given that you're running Debian, you can install the HP Management Agents (for Debian) on the server to obtain a detailed view of what particular component may be causing the issue.
Also see: HP Proliant DL380 G4 - Can this server still perform in 2011?