Make sure to have a Fully charged Baterry, clean Pos and Gound cables real good..if this doesn't work .. jumper the pos to the solenoid to make sure its not the Starter you have just Installed..I have replaced many Bad..New Parts,,made in CHINA
X2. key switch and connectors would be standard procedure to check next. Always work cheap to expensive unless your 100% sure then skip ahead.Starters for those aren't cheap, i'd start with the solenoid first, since you got it to engage when you bypassed the solenoid.
Just my opinion