There's really no lazy "out" here. If you're willing to invest in a decent midrange GPU you'll need a good PSU. A 300-400W won't be that expensive, given everyone is looking at 500-700 (or more) these days.

You get what you pay for though. Wattage is not the way to select good PSU's, stability and features is (myself, I like modular cabling). A good guide:

PSU 101

It's really not that hairy to replace it - just write down all the connectors and their orientation before removing them, google a basic tutorial on the web, or chat up someone local who can replace it. Just make sure whatever PSU you buy fits the HP's form factor; maybe the HP website has upgrade suggestions.

I suspect HP may use a proprietary power supply. Don't know.
How can I found out?

I later found a website selling replacement HP computers. They had mine listed and the replacement was an ATX. Now I need someone to do it. I know it is not hard but that and motherboards are only things I haven't done.

But I am still looking for a 300 watt upgrade video card. I ain't playing doom and I don't need anything that special.

You can probably get by with your 300 watt PS with a card requiring 350w. 7600gt is a good med-range card for a real good price which requires 350w. It running just fine with my 300W PS for now but I'm planning soon to replace it. In general the hotter the GPU runs the more watt it's demanding so if you find you are running games working the card hard then you really need to change your PS soon.

So the more intense the graphics processing the hotter the GPU will become, and thus the more power it needs?

In general, though heat is actually a function of power consumption (which varies from card to card, but generally scales with workload) rather than the other way around.

If my computer is underpowered will the GPU underpreform?

More likely it would become unstable or simply not work.

I've been waiting for about three hours now and still no response from HP regarding my power supply rating on my Pavilion a1410n.

There's no label on the PSU itself?

Guys, you're really going overboard on this. There is no way in hell that any graphics card requires anything near 300W. What you're looking at is actually the "recommended" total system power requirements with the card in question installed. All this will be dependent on processor, memory size, speed and number of hard drives and other peripherals. It also includes a significant amount of "headroom". This worry about a 500W PSU is what I like to call "Gothic" engineering where no one really knows what the requirements are so the beef up everything to the point of absurdity.

I did spend some time chasing it down a bit. The problem is that the graphics cards give this ambiguous system requirement but don't actually specify the requirements of the card itself.

For example a BFG GeForce 7950GT, which is a pretty high end card, "recommends" a 350W PSU with at least 22A of 12V, but if you use two 7950GT's they "recommend" a 500W PSU with at least 28A of 12V. The only information that's certain is that a single card won't draw more than 6A of 12V which is only 72W max. However, they don’t bother to spec the 5V load.

I have an HP Pavilion d4650y with a GeForce 7600GT, a 2.4 GHz e6600, 2GB of DDR2/600 ram and a 250GB, 10000RPM SATA2 drive. All of this is with a 300W power supply. There is absolutely no doubt in my mind that 300W is totally sufficient for this setup. In fact the 300W is perfectly capable of running two GeForce 7600GT in SLI mode with everything else in my system the same. There is no reason to run out and buy a new PSU.

I would recommend an ATI X1600XT. It is one of the better mid-range cards (I use one myself). It should work ok on your system. You mentioned that you don't have a computer supply near. Buy online. You might try Newegg.com. They have a good selection, excellent prices, and their customer service is second to none. They have a Sapphire X1600 listed for 90 bucks. You can also find a 400+ watt Thermaltake power supply for $40. What the above posters say is absolutely true re: changing it yourself. One of the easier things you can replace in your computer. Hope this has been of some help.

However, the processor power is not pulled from the 12V supply, it's most likely pulled from the 3.3V rail or less likely the 5V supply.

This used to be the case, but current-generation CPUs do generally run on a dedicated 12v line rather than the 3.3 off the ATX connector like they used to (largely since it's easier to handle the higher voltage/lower current line when it has to be regulated down to 1-2v anyway, AFAIK). The 3.3v and 5v lines are actually not used for many things any more--most components are centralizing on 12v, so it's even more important now than it used to be.

HP has been known for not putting much of a PSU in their PC. I guess it's their way of cutting corners. IIRC My first Hp a few years ago had a weak 200w Psu.

My old system (Gateway) had a incredibly wimpy 160W PSU. Then when I upgraded to a 350W to support the Nvidia 6800AGP board, it generated enough heat to crash my computer whenever I loaded up a graphics-intensive game. ($30 more smackers for an Arctic Cooler ducted GPU heatsink).

As you can damage a GPU board with a wimpy PSU I'd invest in a decent one (that's 300W (at least)and quality amperage), m'self.

Just to add Mumblefratz... I went to HP and checked out your system specs. You at least got a 350w psu with your model, whereas mine is only 300w. It didn't specify anything with regards to the amperage however. Just to be safe I am going to upgrade my psu to around a 400w or so set up. I know about the amperage ratings and getting what you pay for so I believe I am pretty well informed to go and buy one. I appreciate the comments regarding this, but I would rather shell out 100.00 or so now and be safe than find out the hard way.