98 Dodge Stratus Startup problem after replacing battery

I replaced the car's battery yesterday afternoon. This morning when I
started the car, the engine idled very roughly, almost like it was
going to stall. I gave it gas to keep it from dying out. This lasted
for about 15-20 secs. About 10 minutes later, the car was running
fine. After the 45 minute drive to work, I turned the car off and
restarted it and everything was back to normal.

Has anyone heard of anything like this or what it could possibly be?

History:

I have a 98 Dodge Stratus, with about 56K miles on it. I have the 2.4L
DOHC engine in it. Two days ago, I went to start the car and the
engine wouldn't start. The lights worked, the horn worked, the radio
worked, etc. But the engine wouldn't turn over. It would almost turn
over, then I would hear the clicking from the starter engine. I even
tried jumpstarting it from my wife's Honda PRelude. Still no luck. So
I figure it must be the battery.

I replaced the 4 year old PowerEdge battery the next day. The battery
must have been leaking battery fluid because there was battery fluid
all over the top of it and in the battery compartment. So I cleaned
the battery compartment out and replaced the old battery with a
DieHard. After replacing the battery, I tried starting the car a
couple of times and the car started fine. I let the car run for about
15 - 30 seconds each time. However, no rough idle or anything.
Everything seemed fine. And then the problems this morning.

 

Some of the engine settings were lost when the battery was
disconnected for replacement. They were re-learned during the 45
minute drive.

-Kirk Matheson