I agree that 13.25 volts may not be the optimum charging voltage but dont think with 13.75 running voltage that its the actual fault you are sufering from. So if you hade the car running and when you parked it the battery voltage was good then read on.

This is an easy way to aproch a no cranking diagnosis even though its harder to write it up then it is to do it.

1. At night make sure the battery has a full charge. In the morning before you start the car put a volt meter on the battery if you dont still have 12.something for voltage suspect the battery.

2.If the batt. voltage is ok then leave the hood up and place the meter where you can see it from the drivers seat then turn the key on it shouldn't affect the voltage much then watch closley as you try to crank the engine if the voltage drops (way) down and the engine doesn't crank you have a battery problem or the starter is drawing to much amperage. If the voltage doesn't drop skip to #3 if it did keep reading.
If that is the case then you need to boost/jump start with a amp. meter on the battery cable to see how many amps are passing through the cable when cranking. I would think 300 to 350 would be your max# if the amp# drawn from the battery is lower than that when it was boosted/jump started then the problem would be that the battery wasn't capable of supplying the amperage that the starter needed to crank the eng.

3. If the voltage didn't drop when you tried to crank the engine then that meens that somthing like the starter sylinoid/ignition switch/bad wire/ relay/etc never gave the starter the comand to crank the engine that would make 300sel(88) the hero of this thread. lol... There are a few ways you can go about it but I would just go to the starter and find the exciter wire for the sylinoid there may be more than one small wire sorry dont know the color of hand but when you test it remove it from the starter and place meter on it and if your meter leads are not long enough have someone crank the motor. If it has power when the key is in position #2 then its the wrong wire if it only has power when the key is turned to the cranking possition then the starter is the problem if the large 6.gauge wire has power also(sorry forgot to mention that first)
If you never get power to the exciter wire then you will need to go to the switch plug and check for power there if there is no power in the wire there than its prob. the switch if there is then its poss. relay/wire and remeber you had mentioned wiggling the shifter? Not sure your model has a nutral start switch but wouldn't be suprised if it did.

OK well that should keep you busy for a while and post back with the good or bad news.

Sorry everone for the long post but some things have to be said completely to minamize confussion.

Dave..................