Glad to hear you've the problem. It would be one thing to know immediately that: You need a battery, and then go and buy one. It is amazing how much we can go through just to confirm what the car needs!
Definitely figure out the battery vent. I am not familiar with your car. Is the battery under the rear seat? If so, you WANT the vent connected. The by-product of a battery is hydrogen (yes that explosive gas, hydrogen)
Story? Years ago a friend who worked with me at a Porsche shop was charging the battery in the front trunk of an old 356. The hood wouldn't stay open so he used a short stick to prop it open. He let the battery charge for four or five hours.
Later when he checked the battery and it was warm, he pulled the battery connectors. There was a spark that caused an explosion that blew the hood of the car and my friend across the workshop. He was OK. Car was not.
'03 E320 Wagon-Sold
'95 E320 Wagon-Went to Ex
'93 190E 2.6-Wrecked
'91 300E-Went to Ex
'65 911 Coupe (#302580)