If there is no clicking, and you have verified that it is not a fuse or relay, check the wiring for the plugs near the battery tray, there are people out there that don't know shit, and could have wired the swap wrong. If you don't wire those plugs correctly (or just plugged the plugs in from the sr into the ka plugs), the car will act as you said, with accessory stuff getting power but no turnover or clicking at all.
check the wiring here v most of it is color to color vvv
http://www.frsport.com/SR20DET-Swap-...SR20_t_26.html
Shouldn't get a new starter until you have verified that that was done correctly