Add-on video card help

Hi all. I got my hands on a HP Compaq 6200 Pro SFF (Core i3 3.1GHz, 8GB RAM). This PC is about 4 years old but my current PC is about 7(+) years old. The specs on this HP are a good bit better and I'd really like to find a graphics card that'd work in it and replace my old PC with this less old PC. It does have a PCIe x16 slot and the case is half height so it'd have to be a low profile card. The video card in my current PC is a Radeon HD 6600 with 1 or 2 GB RAM (can't remember the type - GDDR something or other maybe).

A huge problem with the HP is that it has the stock power supply, a 240W one. I need to find either a video card that's as good or better than my current one, that I can get low profile, that doesn't require external power, and that will work with this 240W power supply, or I need to find a replacement power supply that'll fit in this HP case that offers more power.

I really don't want to go the route of cannibalizing parts from the HP (the processor and the RAM specifically) because I'm not interested in building a PC, but I will if it just won't be possible to get my hands on a video card that will fit in the HP, work with the 240W power supply, and provide at least a little bit better graphics than the Radeon I'm currently using.

Any thoughts or ideas?

Even the Radeon 6600 required a PSU of 350W, so finding a faster, low profile card that runs on 240W is doubtful. After a quick look on Newegg, I didn't see anything lower than 300W, even for slower cards.

What are you trying to do with the video? Gaming?

The PSU is proprietary, so you won't find any upgrades either.
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Yeah, my current PC is a home built system that's over 7 years old. It has a 500 or 600 watt psu in it and that Radeon card as well. It's okay for gaming, older games of course. I was hoping to be able to use this HP with an add-on card to replace my older rig, incluidng for gaming. If I have to go the cannibalizing route I will. I was just hoping to not have to.