Why will Brother MFC 8460N not operate on network? A brain teaser!

I'm hoping there's some real networking genius out there, because neither Brother nor Apple can figure this out.

Here's the hardware: MacBook Pro, running OS 10.9 (Mavericks).

Brother MFC8460N printer.

THE PRINTER WORKS FINE WITH THE USB CONNECTION, both printing and scanning.

The printer will NOT print on MY network. It operates fine on another network, with this and another computer.

Here's what I've done (not necessarily in order, but attempting to be so):

Downloaded & installed all latest software and firmware, both from Brother and from Apple.

Pinged the printer via Network Utilities, per Brother FAQs. Report was fine.

Used different CAT5 Cable.

Connected CAT5 cable directly computer-Printer. (To eliminate question as to whether it's a router problem). Still didn't work.

Uninstalled and reinstalled software multiple times.

Cleared the Preference file.

Created new User account and installed printer there.

Tried to print with Sharing on, and Sharing off. No difference.

Reset and reinstalled printer.

Tried an IP install, using the printer's IP address.

I've been walked thru this by Apple tech support. I know I've installed correct drivers, etc.

Here's the irony: on another network, this computer-printer combo works fine, with no setup issues. Plus, I've recently installed the same printer drivers on another MacBook Pro, and the printer worked fine.

I had the same problem with Snow Leopard, and upgraded to Mavericks hoping it would resolve. It didn't.

I've had long talks with both Brother and Apple--even got kicked upstairs to a specialist at Apple. No one can figure it out.

Can you???? Thanks!