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I'm looking at building a "Zotac ZBOX ZBOXHD-ND22-U Intel dual core CULV SU2300 NVIDIA ION graphics processor" to replace an old (very old?) Pentium 4 1.7 Ghz machine.

Can someone give me a very rough estimate as to how much faster this Zotac would be to the older machine? Something like 2X or 2.5X faster.
I'm assuming that an dual-core Intel Celeron at 1.2GHz beats a 1.7 Ghz Pentiou 4.

At this point a damn Atom would beat that CPU... That's a major speed up, and with general PC usage the second core will help a ton.

Essentially, you're looking at a gigantic boost here, even with the low clockspeed of the replacement CPU. The Willamette Pentium 4s were just... terrible, horrible CPUs. You're looking at likely a 3X speedup, not counting the second core.

The Core 2 era roughly doubled IPC over the P4. I recall the 1.86GHz C2D being faster than the 3.4GHz Pentium D (dual-core P4). Then the 45nm Core 2s improved on that further.

Along with faster memory, faster drive, etc, I'd say you're looking at maybe 4x faster for just one core and 8x faster if what you're doing uses both cores.

That processor (I've got it in a laptop) is not amazing but it'll be lotsandlots faster than your old P4, and the cooling will be a lot quieter to boot.

Here are some results comparing a Pentium 4 660 (3.6Ghz with HT) to a Celeron E1200 (1.6Ghz dualcore):

http://www.anandtech.com/bench/Product/92?vs=71#

You'll be fine.

Okay, so maybe 4-8x faster was a bit of an overstatement

maybe, but a 1.7GHz P4 is probably a Willamette core and it's using either RAMBUS or PC-133, whereas the Pentium 4 in the Anandtech link is probably using the same platform as the Celeron just to make things easier to test. So it's got wayyyy more memory bandwidth available.