Lensman:
part of what you post is very normal, only a few details seem odd.
first - pentium D as i recall was a 64 bit cabable proc, other Pentium 4 generation chips are also 64 bit.
just that few folks ran x64 os on them at the time. so you have a P4 and thats 100% normal.
now whyen you load an OS on a 64 bit system the default is to run in 32 bit mode unless the boot loader tells the system to "go 64". that was done so that 32 bit os packages still would load w/o problems.
3 gig and 4 gig memory, the 32 bit hardware can address 4gigs of address space but the BIOS and stuff like video cards, usb controllers and the other bits you need to use the cpu have to get some i/o addresses.... way back when the 286 was designed they figured that 3 gigs was good place to start tossing that stuff as it was way the heck up there and back then you could not even buy 4 gigs of ram and fit it all in a desktop pc case 
later some system boards had the option to map that hardware to the top end of 4 gigs to give a 32 bit system a tad more ram to use.
even with a 32 bit os the system should be able to id the cpu as able to run 64 bit.
the remaining things that i can't speak to are loading 32 but running 64 bit stuff... that does not sound right...
what do you see in task manager ?
any processes listed with names like "iexplore.exe *32" ?? if you see that then i'd say you are running a 64 bit OS.
what about the program files folders ?
do you have one or two of them ?