There are a couple of possibilities here. The first is that the transmission control unit is not working correctly, preventing the transmission from going into gear. You can find out if this is the case by having a technician run a diagnostic with a OBD-II scanner. The chances are good that when you get the read out you will see one or more transmission-related errors.
If it is the TCU, then your best course of action is to have it reset. You can try it yourself, though I wouldn’t recommend it, unless you feel very comfortable doing this, by disconnecting the negative cable from your battery and keeping it off for several minutes. Once the time has passed, carefully reconnect and wait to see what happens. The TCU should have been reset and the problem cleared from the electronics.
If the problem persists, of course, don’t forget to take a look at the tranny fluid level. Many times, that is the prime culprit. Indeed, I would recommend checking it right now, if you have the time. Don’t forget to let the C280 come up to temperature and then take your reading. If it is the transmission fluid, you will see that it is on the lower side of the dipstick, likely reading add fluid. If it is, carefully add fluid until the transmission is refilled. Don’t use anymore than necessary because an overfilled transmission causes its own headaches.
One other place to check is on the mechanical side of things. It is quite possible there is a problem with the differential. The driveshaft and powertrain are working correctly, but the differential is not doing its job by taking the input from the driveshaft and turning it into output for the half-shafts to which it connects. If this is the case, you are looking at about a $1,800 job, depending on dealership or shop location.
Please let me know what happens as I am on here several times daily to keep track of things so I will answer shortly. I also like to see what happens and enjoy helping readers.