truck want stay running

I had a problem with my 02 dodge ram 4.7 liter. I put my key in the ignition, crank the truck, cranks fine....as soon as i let go of the key it goes dead. Every time does this. I cleaned my battery terminals really good, changed plugs, done all the maitnenance. Still doing it. My last straw then it goes to the shop. Any advice would be greatly accepted. has 40,000 miles on it. Oh yeah. Checked battery and getting 13.4 volts and took to autozone and it tested good.

I had a similar problem today after I drained my battery and then jump started it. My battery was good all day until around 6 PM then and then the whole truck gave out and would not stay running after jump starting it again. I took my battery out and took it to advance auto parts they were gonna test it and I said don't bother just give me a new one. Now it works perfectly fine :-). I have an 01 battery. so my suggestion would be to get a new battery and try that out. I bought a Yellow Top optima but you wouldn't have to go that far on the battery. as long as the rating is high enough.