The electronics behind the battery shouldn't affect starting or running. The injection pump is mechanical in nature.

Just because you have fuel in the tank doesn't mean you have fuel being injected. If the block is warm and it's been starting fine, you likely have air in the lines or a fuel leak. Crack the injector lines and see if they're spurting fuel.

Barring anything else, try spraying some WD-40 (don't use starting fluid) in the intake and seeing if you get some attempts to fire. If you do, you know you aren't getting fuel delivered to the cylinders.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]