Thanks, Computer_Commando
From the link uou gave I found:
Celeron Dual-Core desktop family replaced single-core Celeron 400 series microprocessors, that were released in the middle of 2007. First dual-core Celerons were based on Allendale core, which, besides the second core, had practically the same features as single-core Celeron 400 series CPUs
That is a key bit of information. The motherboard was made before 2007, so was never sold with a dual-core Cleon. Yet the Celeron was listed by somebody on the Dell forum as a possible replacement that would give me 64 bit.
So maybe I should have tried a Celeron instead.
EDIT: I did the Dell site with the tag. No recommendations from Dell. But the social forum had this question posted sometime ago and said the fast Pentium D will crash the system. Too fast for the 945 chip set.
In a few days I will see if the2.8 GHz Pentium Ds In ordered will work.