It may take a little more effort to narrow the problem down, but the very first thing you need to start off with if you're convinced the battery is good - is the battery connections.
It sounds like they are dirty and not making a good connection to the battery posts. The supporting evidence is your being able to start the car with jumpers, which grab onto the battery cables directly.
Whether it is ultimately the cause or not, you should take the battery cables off and clean the battery posts and the inside surfaces of the cable terminals until they are shiney. Then reassemble and coat with something to prevent corrosion. I happen to like regular grease, thinly spread.
If this doesn't help, then the next place to check for corrosion is where the ground cable hooks to the chassis - clean that too.
1982 300D at 351K miles
1984 300SD at 217K miles
1987 300D at 370K miles