Hi, bq_32 -
The keyboard model m2452 was the standard keyboard that came with late model G3s and early model G4s. It should have no problem being used with a 350MHz G4, which is either a G4 (PCI) model or a G4 (AGP) model - both of those came with that keyboard model.
Check the USB ports for damage (sprung contacts, for example) and the keyboard's cable for damage (contacts in the connector, damage to the wiring in the cable). If you are using the USB extension cable that came with those models for use with the keyboard, try removing it from the config - they have been faulty.
If you have connected other USB items, try removing them. Specifically, remove anything attached to the keyboard, including a mouse - the G4 has two USB ports, so in a basic setup the keyboard and mouse can use separate ports on the back of the Mac.
Article #TA26015 - Apple Pro Keyboard: Devices Connected
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Since the machine is an older model which you recently acquired, it is reasonable to not trust the health of the internal battery. When that battery is too weak or dead it can cause booting and power-on anomalies. The expected life of that battery is only about 4 or 5 years under best-case sircumstances; when a machine is left unplugged for a while, its life is greatly reduced. Replacing it on a used machine is a good thing to do. You can get a replacement at places like RadioShack for about US$17, cheaper on-line.
In the process of doing that, reset PRAM and PMU -
Article #HT1379 - How to Reset PRAM and NVRAM
Article #HT1939 - Resetting CUDA/PMU
