Good graphics card for media center but NO gaming

First off, you definitely want to verify if the slot is 2.0 or not (I'm guessing it's not). It can make quite a bit of difference if you're willing to spend just 20 or 30 dollars more for a card that can make quite a bit of difference. The x-1950 is just a PCI-e card so you may just want to replace it if you're getting what you need out of it.

If not, the 8 or 9 series from NVidia are getting really cheap and you can always find some really good deals in the 3000 or 4000 series from ATI. For media center playback, you don't need the "latest and greatest" as you probably already know.

The HD 3450 will be fine. No real need to worry about whether it's PCI-e 1.0 or 2.0.

Yes, PCI-e 2.0 cards can be used in PCI-e 1.0 slots. However, if you do, it will pretty much ALWAYS require you use the external power connector; I don't think that the 3450 actually even has one to use, so in either case, it wouldn't matter.

And yeah, that card would be plenty tons enough, since you make no mention of dealing with high-definition video playing. (i.e, Blu-ray) That could require a bit more processing power, but for just watching TV and powering a massive monitor, the 3450 would be sufficient. Plus, it'll use less power than your old X1950, and chances are good you could even find a 3450 with passive cooling, hence cutting the noise level a good chunk.

The HD3450 does n`t NEED an external power connector, it`ll draw all the power it needs from the PCI-E slot.
If there is enough power for the card, any PCI-E card will work in any PCI-E slot and the HD3450 draws much less power than a 1900 and will work perfectly in your system (and draw less power, which is good).
There should be no problem with either HDDVD or Blu-Ray playback as the HD3450 handles decoding and playing of both media with minimal use of the CPU.
Note; HDDVD and Blu-Ray require HDCP compliant displays as well as output (graphics cards). HDDVD and Blu-ray require suitable drives, normal DVD drives will not work.