Found some older posts with similar problem but no conclusions.
Twice this month I've been unable to shift out of park. Weather was around 15-20F
My battery is definitely on the older side (8 years). i suspect the car is detecting a weak battery and wont shift until the alternator charges the battery for 20mins?

- car starts but won't shift out of park. I had to idle it for 20 mins and then restart until it finally shifted

- windows, lights etc still work

- brake lights still work

 

More likely something in the safety or locking mechanism is hanging ("freezing") up. My battery was weak and it wouldn't start at -15F, but at -5 it was crank it up and go. Even at -15, as soon as I jumped it, everything worked.

 

Take a look at this video, might lead you to something. X30/21 Drive train can voltage distributor might be defective. Don't know were it is in our x204 model but in this video, it is in the passenger side. Seems to be a common problem for Mercedes. Hope this help.

 

“My battery is on the older side” no your battery is barely alive , keeping an 8 year old battery isn’t smart. Your just asking for trouble. Low voltage can also damage electronics. a new AGM battery is a good idea.

 

2015 GLK350 started similar behavior. ECO Start/Stop also stopped working. No real diagnosis was done, but 5+ yo main battery failed load test at B Service. Replaced main and aux batteries and problems went away.