An important tool for hardware problems is the Apple hardware test CD. Unfortunately the test for iBook models 300Mhz and 366Mhz without Firewire is not available.
Since the test CD supports only certain models, one should pay attention for to the correct revision number. iBook hardware test CDs with the numbers 1.0 to 1.2.4 should function on the 366Mhz and 466Mhz Firewire models. If one wants to go safe, one selects the extended test routines with continuous loops.
Some RAM errors are identified after some dozen runs. A free Download from Apple (Wayback machine) of the hardware test for older Macs is available. You can also look for a original CD at ebay.com or contact an authorized Apple dealer who has access to these resources.