From what I can remember, celeron 370 should come in two flavours. The PPGA ( plastic pin grid array )older type, and the fc-pga ( flip chip pin grid array). I think the PPGA went up to about 500Mz and the fc-pga went to around 666Mhz.
The problem may be that the older chips worked on a core voltage of 2.0v, while the newer one just worked on 1.5v.
They should all run on the 66Mhz bus, but the architecture is also different. The older model was based on .25 micron and the newer 0.18 micron.
So if you are trying to use a newer 370 chip in an older board, it probably will not work due mainly to the difference in voltage. You would have to match up each chip to each motherboard. That would mean studying the manuals.
Did you manage to get a few beers out of the last one? ;-)