The Motherboard is considered the 'Building Block' of the computer.
From it all hardware components are supported.
Processor, Ram Memory, Harddrive, Optical Drive/s, and add-on expansion slot cards.
A graphics card (Video Card) being one.
You need a graphics card that the ECS 945GCT-HM,
or also stated as HP's Livermore8-GL6; will support.http://h10025.www1.hp.com/ewfrf/wc/document?docname=c01237572&lc=en&cc=pt&product=3632125#N33
The motherboard chipset is an Intel 945GC,http://en.wikipedia.org/wiki/List_of_intel_chipsets#Core_2_chipsets
According to Intel came out the first quarter of 2005,http://ark.intel.com/products/34505/Intel-82945GC-Graphics-and-Memory-Controller
The year PCI Express 1.1 technology came out.
PCI Express 2.0 technology didn't come out until 2007,http://en.wikipedia.org/wiki/PCI_Express#PCI_Express_1.1
Will the ECS 945GCT-HM support graphics cards based on the PCI Express 2.0 technology?
PCI Express 2.0 technology IS backward compatible, with PCI Express 1.1 technology.
You just won't get the full capability of the PCI Express graphics card; based on the PCI Express 2.0 technology.
Will you notice? Doubtful.
From what I have seen listed in reviews on the graphics card, I would not suggest a graphics card based on the PCI Express 2.1 technology.
Reviews suggest it doesn't 'play well' with a motherboard using the PCI Express 1.1 technology.
There is another thing to consider; Power Supply
Most decent graphics cards require a minimum Power Supply wattage, of 400 to 450 Watts.
This Power Supply requirement isn't just for the graphics card.
Graphics card manufacturers base it on a test computer system.
One they put together with a powerful Processor, high performance motherboard, 2GB's of Ram Memory (At least), optical drive/s, harddrive, and the graphics card. (Plus allowance for computer case fans, etc)
If you're running a 300 Watt power supply, this = No.
(Yes, even though AMD ATI Radeon graphics cards, are touted to use less power; 400 to 450 Watts is still the limit for a decent graphics card, from them. Unless you want to run a simpy PCI expansion slot graphics card, or budget/starter, PCI Express graphics card)http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=4501123&CatId=7387http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=2555929&CatId=7387