Check for 12V at the starter when you turn the key. If you've got that, there's your problem. If it's on it's way out, sometimes you can just bang on it to jar it a little and it'll spin; it would still need replacement, though.

It sounds like the tire & alarm thing is just a coincidence.

__________________
A.S.E Tech A1,A6,A7,A8 & MVAC 609 + EPA 608

Unless stated otherwise, any question I ask is about my greymarket 1985 380SEL.