The alternator must be over charging or under charging the battery. Next time you get it running, put a volt meter on the battery while its running. You should read 13.5-15 volts

 

I very often see people replace the battery and the starter without replacing the battery cables. If you have not replaced both cables within the last few years I would replace them. Make sure that your ground is clean and bright. Also, there shoud be a ground between the block and the body that needs to be clean, too.
Very often battery cables look good, but if you pull back the insullation it is corroded...if it is not that bright copper color, replace it.
Frankly, I have a hard time finding ground cables that I like, so I make my own from #2 cable and solder the ends on myself, but I have a winch and need the extra load capacity.

 

We haven't replaced the alternator. Its worth looking into...
We have replaced the battery cables within the last year. We are going to check the grounds again.

Our short term fix: buy a 1992 c1500 with a 350 and a crew cab. It hasn't had an inspection sticker since 2010. We also had to replace the battery and put air in the tires to drive it home but it was only $500 and it runs. It needs a little work but not its too bad. Once we finish this we will be back on this truck to figure out its problem.

 

I have been reading on this post about a year now. No offence but I don't feel any smarter for it . It isn't the battery , it isn't the starter . It is a direct short between that terminal that is circled on the junction box and the key switch in the column . My son had the same problem on his 93 . He took a lot of things apart without me and couldn't figure out how to put it back together and got rid of the truck . A elderly man I am helping right now has it on his 1989 chevy. This is the same problem and I believe it may not be uncommon . It puts heat on that fusible wire . If you hold the ignition down a couple seconds it will burn that fusible wire. I had the starter off and tested it manually on the battery and it kicks in fine. Surely theres a chevy man that can post the answer. I have a feeling that the answer gets found and the person hunting it stops posting because he needs help no longer .

 

I have shorted across the starter to solenoid with a screw driver and started it. Now it wouldn't shut off with key . I must assume it is in the wiring in the steering column . Maybe this will be some help to somebody in the future

 

Hi have you found out what the problem was having the exact same problem on my 88 Silverado k1500. !???