Starts and runs then stalls

[tahoelt53]

I have a 2004 tahoe 5.3 v8, it was running fine then I accidently let the battery run out. I jumped it off but it seemed like it was taking an unusually long time to charge enough to start ,then after I got it started I was letting it idle to charge. after running for a few minutes it sounded like it was about to stall out like it was running out of gas for about 2-3 seconds then ran fine. The next dayh I drove it to work and it would run fine then when I would pressed stutter like it was trying to stall out then it was fine. On the way home it died after stopping at a red lighht when i pressed the gas to pull out. I got it started back and drove on home. Now if ii let it idle it will run for about 5 or 10 minutes then stall but will start right back up and it keeps doing this it also has no check engine light

 

[tahoe_driver]

hmmm, seems to be that the alterinater went bye bye, i'd have it tested first though