I agree with building a new system for the same reasons given, but that's a MUCH bigger endeavor (not to mention MUCH more expensive).
I am shocked - in a very good way - to see the 80 PLUS Gold logo on the image of that PSU. It takes an excellent design using quality parts and refined assembly techniques just to get 80 PLUS
certified. To achieve a Gold rating is even more remarkable - for any supply, let along an OEM.
So I have to say I am seeing HP in a different light and have a much better respect for them now - at least when it comes to power supplies.
My concern is when looking at the computer's specs
I don't see ATX anywhere. :( Since this computer is pretty new from last year, I want to assume this is just a slimline ATX supply. My problem is, I would hate to assume that, then hear you fried your motherboard with a real ATX compliant PSU.
If me, I would connect a PSU Tester
to your current supply. If no errors (except the normal -12VDC missing error), then I would feel comfortable saying you can replace that PSU without going through HP (which would be more expensive, if any are even available).
The advantage of this model PSU tester is that it has an LCD readout of the voltage. Lesser models use LEDs to indicate the voltage is just within some "range". These are less informative, considerably cheaper, but still useful for detecting PSUs that have already "failed" - or in your case, to verify your PSU is wired to ATX standards. Newegg
has several testers to choose from.
Having said all that, how much RAM do you have? If looking to boost performance, depending on your starting point, adding RAM generally provides the most bang for your money - especially if using integrated graphics. And the advantage of adding RAM vs a new graphics card is you most likely won't need a bigger PSU.