Well, starting systems are typically very simple. As you say, it's a battery to starter thing. A weak battery can wear out a starter, constant low amp starting Is not smiled upon by starters. Now with a fresh battery, what do the starting attempts sound like? If it sounds like grinding, then the starter needs to be rebuilt. If its just a click, its the solenoid.

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77' 300D, "Cartman" SOLD @ 150K (didn't know what I had)
83' 300SD, "The Superdon" 325k+ @ 28mpg
95 E320 wagon, "Millennium Falcon" 231k+ @ 24 Mpg
95 E300D, "Sherley" 308k @ 33.69 Mpg, currently anticipating a head
99 Suzuki Intruder "Trudy" @ 45 mpg