Barely able to get up a grade after stopping

[sfdjeo]

My 300SD (305K miles on it) drives fine on flat roads, and fine on grades when I'm moving. But if I get to a hill and have to stop (I live in San Francisco so this happens a bit), when I try to get going again it BARELY can move even when flooring the pedal. If my car is full of people it won't move AT ALL (this happened once and I had to embarrassingly throw it in reverse and do a three point turn and drive down the hill and go a different way). The engine runs fine, I'm wondering if it's my throttle linkage not moving far enough maybe? I'm hoping it's something like this and not a transmission problem. The tranny is a little rough but it never slips or gives me any trouble otherwise...

Anyone else have this problem?

Thanks much for your time everyone!