It's entirely possible your alt. has had it.
Then again, depending on it's age, you may be able to get away with a new voltage regulator. A lot of times, this is all that's wrong. Easy to check.
If the car will start, what kind of voltage are you seeing with the VOM set to the 20 scale, red lead on + terminal; black lead on - terminal?
On a cold motor, you should see 13.9 or better. When warm it may be around 13.5. If this isn't happening, pull the voltage regulator. Easy to do. It takes longer to setup a 300-SEL for this than to actually do it.
- Pull front of car up on ramps.
- Remove large encapsulation pan underneath. 300-SEL pan is secured with four-8mm screws.
- Underneath alternator, you'll see 2 phillips screws securing the VR. Remove the 2 screws and pull out the VR. It comes right out. Look at the brushes - carbon looking and spring loaded - there are 2. When new, they are about 1/2" long. I'll bet yours are worn down.
- If worn down, install a new set. They go right back in without issue.
- Reinstall 2 phillips screws.
- Reinstall encapsulation pan and start up. Check volt on battery now.
Here's a photo of the VR. You can click on it to expand.
http://catalog.eautopartscatalog.com/mercedesshop/sophio/wizard.jsp?partner=mercedesshop&clientid=mercedesshop&baseurl=http://catalog.peachparts.com/&cookieid=1HB00BPJD1HB00BVI7&year=1988&make=MB&model=300-SEL-006&category=F&part=Voltage+Regulator
This part can be ordered online from here and elsewhere or look for a local supplier if time is an issue. The original part is Bosch.
When it came time to replace my Bosch alt., I used an AL166X(100amp) vs. the std. AL66X(80amp). I now see 14.30 on a cold motor. With the 80amp alt., I never saw anything > than 14.0. I'm not sure if the AL166X plug will work on the '88 300-SEL.
My 2 cents.