Motherboard replacement
 

I have an Antec Sonata case with a defunct Gigabyte GA-8IPE1000 Pro G
motherboard that I want to replace. I want to use this computer with a
Samsung plasma TV, a Samsung Bluray player and a Logitech wireless/mouse.
Currently, the player is accessing the internet through a hardwired
router upstairs. I would connect the "ReJuvenated" computer to the upstairs
router and the Bluray player, using a second wireless/mouse and the plasma
TV as a display. At present, I don't need a wireless connection to "RJ"
but replacement of the present video card with one with HDMI capabilities
is desirable.

Any suggestions would be appreciated.

The GA-8IPE1000 Pro G is a mainboard for socket 478 CPUs (older Pentium 4 and Celeron). If you want to replace that motherboard with a new one you also have to replace CPU, RAM. I would recommend to buy a cheap new computer.

Its possible to find a socket 478 motherboards on sale new, 2nd hand they are pretty easy to get. You'd have to be careful though, some socket 478 boards use DDR2, 1 PATA port and have PCI x16 slots for video (your gigabyte uses DDR, has 2 PATA ports and an AGP video card).

It is possible to get AGP video cards with HDMI with newer ATI/AMD cards, but technically they dont support linux (even though they do work with linux from everything I've seen).

+1, though I wouldnt suggest buying a whole new computer. The sonata case at least is worth hanging onto, if it was me I'd install new parts into that.