I'm not sure the PSU is enough. Use some jumper cables from a car battery. Inrush current on a starter can be huge and the PSU wires are quite small. Also, note that the PSU's 350W is spread across the 12 and 5V rails. You can't get 350W from the 12V rails alone, maybe 200 or so tops. The label on the unit will tell you what it can do.
2005 Yamaha Zuma YW50, 2009 Kawasaki Super Sherpa KL250