I have the following Subwoofer in my home powered with a modded PC ATX power supply but isn't enough to deliver the right current to the amp and the thin yellow 12v wires get too warm at times.
I'm surprised the wires are overheating, but yeah... I think most of the power (wattage) for a computer power supply is from the 5V output.
The regulated power supply I found:
But I need something capable of running 40A 750W peak, 250W RMS.
That would probably work fine... Normal program material has about a 10:1 peak-to-average ratio so at 750W peak you're only consuming about 75W on average. There is some inefficiency in the amplifier so the power supply need to supply a little extra current but in the real world you should be fine. But you do need the current on the peaks so you'll need something "bigger" if you want to be sure you're getting full-power.
[u]Here[/u] is a higher-power power supply. Or, [u]Digi-Key[/u] (or Mouser) sell all kinds of power supplies. The "nominal" voltage of a fully-charged car battery is 14.4V so you could go 14.4V or even 15V and you might get more power (which you probably don't need).
Only question is where and how would I ground the amp...?
The negative power supply output (or common) goes to the ground (or negative supply connection) on the amplifier (powered speaker). There is usually no need to earth-ground the power supply output, and earth-grounding might create a ground loop which could introduce noise.
The DC & audio ground is just a common connection point. For example, the ground in a car isn't earth-grounded, it's just a connection to the chassis/body. If your audio system is earth-grounded there may be a true-ground through the audio cables, but that's not important (unless you get a ground loop, etc.). Sometimes the audio ground isn't connected to the DC ground either.
The power supply's ground terminal (normally connected to the power supply case) must be earth grounded for safety reasons.
I know in order to power the regulated power supply I'd need to strip a kettle lead and use it's pos, neg and earth wires to connect to the supply.
Or you can go to the hardware store and buy the plug & wire, or you can buy a heavy-duty extension cord and cut-off one end, etc.
With these screw-terminal AC connections I like to cover the connections with hot-glue so nobody can accidently touch the lethal voltage. (I'm pretty sure the whole power supply is supposed to be mounted inside another cabinet so nobody can touch it.)