With a judicious use of silly-putty or play-dough both a P4 and an Athlon can be fitted onto any mobo.
Of course if you want them to actually do something other than sit there and look pretty, well that's a whole different kettle of fish-sticks.
If you want the processor to actually work, than an Athlon is way out and a P4 is only possible <i>if</i> it was a P4 Celeron to begin with, which it probably wasn't. But who knows.
If you could tell us the actual motherboard involved it would make a huge difference to the quality of information. Even just the socket type would be ten times more useful than the extremely limited information that you've given.
According to Dell, the Dimension 2350 uses an i845GL chipset. It's a 400MHz FSB motherboard and comes with PC2100 (DDR266) RAM.
The fastest processor that you can upgrade to with that system is a Pentium4 2.5GHz NorthwoodA with a 400MHz Front-Side-Bus. (Not to be confused with the 2.53GHz Pentium4 NorthwoodB with a 533MHz FSB, which this motherboard will <i>not</i> support.)