it would be cutting it very close to 300w at best. now consider that the psu that any manufacturer uses is a cheap piece of crap and has more than likely lost output since, I'd say that no, it wouldn't work. You'd have to replace the PSU along with it. 400-450W should do the trick.
As for your DVI question. Yes it should work fine, so long as your monitor is single link and not dual link.
Your very old tech pc might work with that card, but there are no garrantees. It is 'likely' it will work, but your power supply is feeble at best.
If it works, you will encounter shut downs and boot fails as the power supply dies in 6 months. Then you can have fun starting from scratch.
Yes, it will work, the only thing you need is an empty PCIe x16 slot at mobo.
The only thing to consider would be the PSU, cause the HD6670 needs 400W and 17A minimun, so all depends on your PSU quality and +12v rails POWER, for instance I used to build a lot of PCs with 300W psus from SEASONIC with 24A combination at +12v rails that can easily power that GPU.
I also recommend the GDDR5 VRAM GPU version, as its fasterl than DDR3 VRAM GPU version.
It will work with a single link dvi-d cable as well.
power supplies are universal really. so yeah they will be compatible. unless gateway decided to use a motherboard with non standard power connections. (it should have either a 4 or 8 pin cpu power and 24 pin motherboard power connectors. which all PSUs have). so no need to worry about it. I haven't heard of a consumer pc that didn't have 4 or 8 pin cpu power and 24 pin ATX power connectors. Even my old athlon 64 x2 pc has those connectors.
alright cool, thank you all very much!
and as for another question .. with my computer, is it REALLY worth it to buy a new graphics card for it just so i can play league of legends and some other low graphic games? or is my computer honestly too shitty to be worth it. (note i cant buy a new computer any time soon until i can get a job)
well only you can answer that question. a 6670 would be a huge boost in performance for your rig. you'll still be limited by your cpu (the athlon 64 x2 is getting on in years, still surprises me when i boot up my old one to mess around with tho.) but integrated graphics of that generation are laughable. since you can't get a new pc any time soon, it all comes down to whether it is worth it to YOU.
Your PC is pretty old now, but that doesn't mean that the 6670 is a bad choice for it if you want to extend it's life. if you wanted to play sc2 you'd be able to run at least the first one. My old Athlon rig with an nvidia 9500GT got 25-30 FPS in singleplayer with over 200 units on the screen at 1440x900 at medium and some high settings. so with a 6670 you'd get a bit better graphics out of it (not necessarily framerates but ya). Your CPU will likely bottleneck the 6670 a bit but not by that much.