So there's only four possibilities I see with what you've said so far.
1. Weak starter. The fact that it is new, rebuilt, blessed by Case itself is irrelevant to whether it is good or not.
2. Weak battery. same.
3. Hydraulic, belt, or transmission drag on the engine.
4. Internal engine drag.
No metal debris in the filter suggests the engine is fine, water and empty oil filter is suspicious. You can turn the engine by hand to see the drag on the engine internally, but the hydraulic pump will usually turn fine slowly, so that won't help. Could remove the coupler to the hydraulic pump to try that, and remove/loosen belt to try that.
Given those are the only possibilities I see, swapping the battery is the easiest, trying a new starter is second easiest and most likely. Then other drag issues.
The engine quitting is a mostly unrelated fuel problem in my guess.
I'd look for a mahle/iskra/letrika gear reduction starter, or a cheaper import gear reduction starter if you can't find a mahle.
1. Weak starter. The fact that it is new, rebuilt, blessed by Case itself is irrelevant to whether it is good or not.
2. Weak battery. same.
3. Hydraulic, belt, or transmission drag on the engine.
4. Internal engine drag.
No metal debris in the filter suggests the engine is fine, water and empty oil filter is suspicious. You can turn the engine by hand to see the drag on the engine internally, but the hydraulic pump will usually turn fine slowly, so that won't help. Could remove the coupler to the hydraulic pump to try that, and remove/loosen belt to try that.
Given those are the only possibilities I see, swapping the battery is the easiest, trying a new starter is second easiest and most likely. Then other drag issues.
The engine quitting is a mostly unrelated fuel problem in my guess.
I'd look for a mahle/iskra/letrika gear reduction starter, or a cheaper import gear reduction starter if you can't find a mahle.