Hello there!
In order to manually start up any PSU, you just ground the green wire. Here's the pinout for the G5 PSU-
Power Supply P1 Connector
Pin# Signal Color -- Pin# Signal Color
1 +5Vstb Purple -- 13 GND Black
2 GND Black -- 14 Power ON Green
3 FANtach White/Yellow -- 15 GND Black
4 GND Black --16 Reserved
5 Reserved --17 GND Black
6 GND Black - 18 RTNaud(GND) Black
7 +12Vaud (12V2) Yellow - 19 GND Black
8 GND Black -- 20 +5V sense Red
9 +3.3V sense Orange -- 21 GND Black
10 GND Black -- 22 -12V Blue
11 GND Black -- 23 GND Black
12 Reserved -- 24 Reserved
Power Supply P2 Connector
Pin# Signal Color -- Pin# Signal Color
1 +3.3V Orange -- 9 +5V Red
2 +3.3V Orange -- 10 +5V Red
3 +3.3V Orange -- 11 +5V Red
4 +3.3V Orange -- 12 +12V3 Yellow
5 Reserve -- 13 +12V3 Yellow
6 +12Vfan Yellow -- 14 +12V1 Yellow
7 +12Vfan(12V2) Yellow -- 15 +12V1 Yellow
8 +25V White -- 16 RTNfan(GND) Black
Power Supply P3 Connector
Pin# Signal Color -- Pin# Signal Color
1 +5V Red -- 5 +5V Red
2 GND Black -- 6 GND Black
3 GND Black -- 7 GND Black
4 12V2 Yellow -- 8 +12V2 Yellow
On the first connector, you'll see that pin 14 controls the power on function. Just place a jumper from pin 14 over to any black ground wire (the easiest would be pin 2). Make sure you do this with the PSU unplugged! After setting the jumper in place, plug it in. It should start up if it works. If it doesn't start, you need a new PSU.
If the PSU is fine, you'll probably want to try a PMU reset. This Apple document can guide you through it-
http://docs.info.apple.com/article.html?artnum=86760
Let me know if these solutions aren't effective. We can try some other things from there.