1. Get you battery tested. Probably a dead cell in it. Alt is likely fine.
2. Clean all your cable connections at the battery, and the grounds at the transmission bell housing.
3. You don't have a HG issue. You most likely have a leaking lower intake manifold gasket, coolant elbow, or radiator issue. If the LIM gasket has not been changed, get the updated Aluminum gaskets, grey RTV, some new coolant elbows, gasket kit for up top, some valve cover gaskets WITH the bolt grommets, some coolant and go to town. The LIM gaskets are a known issue on these motors. The HG rarely if ever go, even when overheated.
Search for LIM gasket replacement on here. I know there is a write-up somewhere. Might also be a good time to change plugs and wires if they are getting up there in mileage.
