Who's generic 450 watt PSU. Dells tend to be decent, however if the one in your case is a raidmax i wouldnt run anything more than a 4670 on it. Open up the case and post the current available on the 12 volt rail as that will provide useful information. A 4870 is pushing it for a generic PSU, but you may be able to get a 4770 or 4850.
 

topper743

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Try one of the psu calculators online to help you determine the system useage, I think the a 4870 draws about 130 watts at max load.
 

pcfreak101

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Quick question on sorta the same subject. How reliable are mushkin PSUs? I traded my 400W Corsair for a mushkin 850W. I don't often see them listed in recommendations of PSUs.
 

Gulli

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It doesn't have a PCI-E connector and probably around 230W on the 12V rails, so the most powerful card that will work with it is the HD 4670 (yes, I know there will be people saying that there is also a similarly performing 9600GT Green, but that one is very hard to come by, easily confused with other 9600GT versions, more expensive and it won't perform better, so for frak's sake just get the 4670.)

 
Not a bad base spec on the HP.
I'd say you should get a better PSU, it's the heart of a reliable, stable system and one component you should not really skimp on. Corsair, Antec, Seasonic, FSP, OCZ, Pc Power and Cooling and FSP are amongst the best, check around the E-tailers for the best prices.
If you're playing at or below 16x10 resolution, look at the 1Gb HD4870 or GTX260 and 500W or thereabouts, at 1920x1200 or 1920x1080, the GTX275/HD4890 with 550-600W is a better solution, but check that the PSU has the right connectors to power the selected card, do NOT use molex-to-PCI-E adaptors.