Engine running poorly after battery replacement

I have a 2003 Silverado 2500HD with approx. 74,000 miles on it. It has a 6.0 V-8. A few days ago the truck would not start. When you turned the key it just clicked. I checked the battery with a multimeter and the battery was low on voltage. I jumped started the truck and replaced the battery. Now the truck starts fine but has two noticeable problems. 1. The truck runs poorly at idle (in drive at a stop light for example. The RPM's are very slow at it will almost stall). 2. The A/C will come switch from blowing cold air to hot air and back again. This truck does have a two battery system. I thought the computer might make an adjustment to the RPM issue but it has not.