If you have a 2004.5 LLY, then it is almost certainly an injector connector. You didn't list the codes, but my crystal ball says P0207 and P2146. P0207 says that #7 is the culprit. It's almost always #2 or #7.
It seems that GM wanted to get your attention if there was a problem with one cylinder. I mean, it would probably still run pretty darn good on 7 cylinders. So if 1 goes, they shut down 4.
For me, it was #2 (P0202/P2149). You can search for "ice pick" to get an idea of the problem, and one solution. I stuffed aluminum foil in the connector when I was miles from nowhere. It would go 35 miles and happen again. More aluminum foil and it got me somewhere. Since then, I bought a bunch of cheap injector connectors from Amazon (4 for about $16), soldered a 2-way connector on the harness, soldered the other half of the 2-way connector on a new injector connector. I only did it for #2 and #7. I have lots of spare injector connectors with 2-way connectors. The idea is if a failure occurs on the road, I can just pop on another connector. It's been over 2 years and the cheap injector connectors have worked perfectly.
2004.5 Silverado 3500 SRW 4x4, D/A (LLY), Ext. Cab, Long Bed
engineer837 aux rad, TxC CAI, LBZ MP, Scangauge II, Nicktane aux filter head, KD lift pump, 2008 PS pump, 2011 hydroboost, Frederico Swaybars, Rancho 9000XL, Torklift StableLoads, BFG AT/KO2, Lance 835 Camper often in the bed.