83 300SD Neutral Safety Switch bypass?

I assume you just want to start it up? On a W126... on the passenger side, there are a row of electrical wires below the antifreeze tank... The purple wire is remote starter wire... so you hook up a remote starter to it... and to positive of battery and you can crank it until it starts.

I went to try it but thought I'd give it one more try without doing anything and it started perfectly. All I did was sleep.

It was ungodly cold last night and I'm wondering if the solonoid just froze or something.

Could be... or it could be that your battery is really cold too... enough so you only get a click... Either way, you know what you gotta do... keep an eye on that starter... test your battery and any other things or you are gonna get real stuck one day...