Battery won't take a charge; dim green light from charger

I have a MacBook Pro 13", mid-2012 with a 60W MagSafe.

The battery started acting up, saying it would need to be replaced soon, so I suspect it's dead. I've ordered a new battery, but I'm wondering if there's any temporary fix until it arrives (it's going to be a week before it gets here).

Anyways, yesterday I noticed that my computer wasn't charging. I realized my charging port was loose (literally recessing into the body), so I opened up the back and tightened the screws for the charging port. Closed up the back and still nothing. When I plug in the charger, there's just a dim green light.

I tried resetting the SMC, but when I try to power it on after pressing Shift-Ctrl-Option-Power, it won't turn on. I can only get my computer to work by unplugging the charger, opening up the back, disconnecting the battery from the logic board, holding down power for ~5 seconds, then plugging in my charger (while still holding power). My laptop can work more or less normally, except without any battery indicators, but the fan runs on full speed.

My questions are (1) Any temporary fix? and (2) How can I quiet the fan down?

Thank you for any help you can provide.

P.S. I've tried multiple chargers and multiple outlets, and cleaned my charger & port, so I know those aren't the problems.