The parking brake on my '88 420SEL will not hold on car at all, even on a flat surface. I'm thinking the cable needs to be tightened. Is this something I could do myself? If so, how?

The parking brake shoes have an adjusting star nut as I call it. Remove the rear wheels and turn the rotors and look through the lug bolt holes in the rotor/hub and turn it till you see the adjuster. It looks like a gear. Usually it's located at about the 1 o'clock position.

I think the cable is loose/broken...
 

I don't think it's the shoes, but I'll check that out. I think it's the cable because I can depress the pedal all the way to the floor with very little resistance