OK, you seem certain that it isn't the processor, and you have tried the stripped down boot with no difference. Just to rule out the graphics card in connection with power problems, remove everything, including the graphics card and try to boot. When the PC (or what is left) boots and find no graphics card, it should give you an audible post error, and continue to run in its usless state (i think), until it is switched of.
You say that apart from the mobo & processor the PSU is the only thing that you have changed. If you are confident in the processor this only leaves two things - mobo & PSU.
As jurgen36 and I both seem to know through experience, PSUs can & will provide difficult to diagnose problems (especially if they are ruled out of the equation because they are Antec and/or 350Watt).
The system which gave me problems with an Antec 350W & QTechnology 380W (both split new)was as stated a bog basic P4 with a Geforce4 card and 1 CDROM drive. Your PC has an FX card and two CD drives??
PSUs are a bit like processors in the performance stakes, an advertised 350Watt, possibly gives on average 370Watt,
on a good example more, and on a bad example, possible less that the stated 350Watts? And shitty PSUs, just like anything else will get through the net.
On a last word, to keep the PSU running, there are two lines connected to the ATX main connector plug that are responsible for telling the PSU remain on (from memory, they are a black and a green line, next to each other at one end of the connector(cant remember the terminal Nos), a poor line or connection here could also be causing your problem.
A
on "power supply forum" will give you more info on this.
I could be giving you a bum steer here, but it all sound pretty familiar & I through experience, I no longer class sub 380Watt supplies as consistently reliable on modern PCs.
Hardware is easy, Software is not!