I had the same issue with mine. Never figured it out, since I then got the Macbook I have from ian.finder here on 68kMLA and eventually sold the MDD off to someone on CL, since I have another G4 PowerMac, that being my Digital Audio with 1.2GHz G4 upgrade, which I've owned since 2009. It seemed in my case that it only happened if I didn't use the computer for a couple days or so. If I used it daily, it'd power up no problem.

One thing you probably want to do, if you haven't already, is source a copy of CHUD 3.5.2. Install that. Allows you to enable nap mode, which will quiet the computer down quite a bit. It'll still be loud, but won't be howling at full speed.

-J