It won't work. A Radeon 2900 graphics card requires at least 200 watts. The 300 watt power supply in a HP a6114x won't even have the required connectors, let alone the electrical power required to run the whole system.
It looks like it will fit fine in the space you got and 500W should be good, what is the model and how much can the 12V rail output?
This is with a Intel Extreme Core 2 Duo
But non-gamign it will be fine
6670 will be a better choice IMO