After a replacing my battery last winter, I 've noticed our e320 4matic wagon has been acting up. anyone have ideas on what might be wrong?

symptom 1: the car has a little trouble starting. it will start perfectly, and then immediately shut off. if you tap the gas lightly and rev the engine above 1k rpm, the engine idles and behived totally normally.

symptom 2: our blower motor just stopped working. it was working fine, no sounds, or smells. had anyone replaced a blower/regulator on one of these? anyone got a diagram? there were no bad fuses and all other hvac unctions work perfectly.

symptom 3: the tailgate close assist seems to be dead too. huh!

thanks!