1995 BMW 318 Car Won't Start? Starter. Battery. Solenoid.W

First thing, ensure your battery is fully charged and functional. Also make sure all connections are solid and corrosion-free. If the battery is good and you are getting a "click" that means (most likely) the ignition switch is okay. Now, you need to suspect the starter/solenoid.

You indicated that you "arked" (I am assuming you meant "arc'ed") the starter from underneath, meaning you bypassed the solenoid, and the starter spun freely but did not engage - which is exactly what you would expect.

Sounds like a solenoid problem to me. But, this is a internet forum so, nothing is guaranteed. Recheck power to the starter and if you have power and only get a "click" and then you bypass the solenoid (as it appears you did) the solenoid is the problem (most likely - everything in auto mechanics is"most likely.)

Hope this helps!