dead battery, bad alternator?

My stepson bought a 1996 Jimmy with 180k on the clock. The vehicle was well taken care of for the mileage and seems to run well. The guy we bought it from just put a slew of new parts on it for inspection, including a new alternator and battery. We've only had it about 3 weeks now and its steadily been getting harder to start. Last night I went to move it so I could mow, and it turned over once and then just clicked. I checked the battery and it had 9.8 volts. It's on a trickle charge right now. I'll be checking everything later tonight (if the rain stops) but I wanted to find out if ther are any known issues with the charging system on the Jimmy/Blazer I should be wary of. Any thoughts?

No real issues that I know of. Did you check for an electrical draw on the battery?

I did check. There is always a draw on the battery because of the computer, etc., but nothing extreme. I'm going to reinstall the battery tonight and hope it cranks over. that at least will tell me if the alternator is any good. I'll check all the lights to make sure none were left on. I suspect the vanity lights in the sunvisors may have inadvertantly been triggered, as my stepson just put a sun screen in the windshield. I'll post back later this weekend.

Well, I figured out what the issue was. The door on the vanity light in the sun visor is slightly loose. With the visor pulled down to keep the sun screen in the windshield it allowed the light to pop on. Dead battery after a few days. Thanks!