I could never keep track of which models need a working pram battery to boot, which ones will hang if the pram battery is half-flat, and which ones don't care.

I do believe that a completely dead pram batt will still allow the 3400 to boot, but I am not 100% sure -- I'm relying on memory, and that's a shaky thing.

You could simply leave it plugged in to charge the pram battery and try again in a day or so, or you could disassemble that puppy and disconnect the battery and try to boot that way. Since disassembly requires more steps, perhaps you'll want to try plan A first.