|"I have a Shuttle XPC with a shuttle fd30v10 motherboard"|
Are you sure about that model number? Could it be FD31V10?
"Will this motherboard/chipset support this processor?"
No, the i945g/gz chipset doesn't support the Core 2 Duo.
"the Pentium D has 4 MB Cache and the e7400 only has 3 MB Cache, does that make the Pentium D Faster?"
Have a look at this comparison between a Pentium D 950 @ 3.4GHz/4MB L2 vs a Core 2 Duo E6300 @ 1.86GHz/2MB cache. The E6300 wins in almost every single category.
If a C2D E6300 @ 1.86GHz beats a P-D 950 @ 3.4GHz, it should stand to reason that a C2D E7400 at 2.8GHz would obliterate it! Too bad your board doesn't support it.