1996 Hyundai Accent Wont Start

I have a 1996 Accent and it will not start with the key. No clicking noise. Nothing. But when I take some jumper cables, and connect one end to the positive side, and the other end directly to the stareter, the car starts (if the key is turned on). Even with the ky off, if the cabl is hooked to the solenoid part of the Starter, it still turns over. I put a volt meter on the little plug on the starter and its only showing .6 when the key is turned in the on position. I looked in the manual for a starter relay and is doesn't show one and cannot find a fusible link. Any suggestions? Brand new starter and brand new battery