97 Ford Probe starts but doesn't get any power. HELP!

I have a 97 Ford Probe with 80,000 miles, that has been giving me problems. I live in Indiana and we usually have pretty cold winters which is when my car starts to act up.
I went out to start it on Saturday and it wouldn't start at all, it would just crank. We jumped it and immediately it started and ran fine. I took it to Battery Masters where they said my battery wasn't keeping a charge and replaced it. I thought it was strange because when my car was on, it said my battery was normal. They also said when they replaced the battery my car acted like it didn't want to run at all.

I drove it home and could not get any power at all. I literally had to floor it to get it to even go. When I got home, I turned it off and turned it back on. It started up but died immediately.

On Tuesday, I went out and started it and it started fine, drove fine, everything was perfect!

On Wednesday, I went out to start it and it started fine but as soon as I started to drive it, I noticed it wasn't getting any power again. When I'd stop, it'd act like it was going to die, so I would throw it in neutral and give it gas, which seemed to work alright.
Still. It would barely get any power and just did not want to go. I had to floor it the whole time to get it to go anywhere and then it started to jerk really bad.

I took it to our mechanic to have it looked at, only to be told that they are booked for the next week. So I made an appointment and went out to start my car and leave but it kept dying. It would start up fine but die soon after.

I am thinking it's the alternator but I'm not sure since it says the battery is normal. Unless that gauge is broken but it seemed to be working before.

Any ideas?