If you get an amp, and was going to run it off a new headunit, then the best way is to connect it through rca/phono leads. Most new headunits come with these on the backso you just run a pair of them to the amp from the headunit along with a remote switch.
On that current plug youve got, im thought the gray and white cables were front right and left, and purple and green rear right and left, but depends if you still need them after youve put the amp in.
if you want to run it temp,the get a battery ( something like a AA or 9v ) and put that to the cables connected to the green and purple cables from the plug, they'll crackle and you can tell which ones are which then if there not working at the mo or even if they are wired in all all. The power supply ( red and yellow cables) might be salvagable if you can test it, with voltage tester, but up if you if your gunna start again!