Ok, I have done a couple of more tests.
With a piece of thin bubble wrap between the cover and the slots/modules, the result is the same no matter which slot I install the "new" module in. Fan spins, system is on, but black screen and no boot. This happens no matter if the RAM slot cover with the bubble wrap is present or not. So I guess yesterday's scenario with the 1-3-3-1 beeps was probably just a result of me not seating the module properly. The old module still works from both slots.
The sticker on the "new" Micron module says:
512MB DDR, 333, CL2.5
The individual IC chips are all marked:
This seems to be a DDR PC2700 333MHz module, like I am supposed to have. My knowledge is not extensive enough to say anything about the CL value, though.
(Ok, so the Micron module says: "Country of origin Singapore." So much for supporting local business.
We have a Micron manufacturing plant here in Boise)