I replaced the battery in my 1996 Blazer because it would be dead when I went to start it. For some reason the new battery won't stay charged either. I read the forum and started the truck, removed the negative battery cable and it kept running. What else can I check?

 

You need to determine what circuit is draining the battery. To do this, you need a multimeter. With the key off, remove the negative terminal from the battery and put the multimeter inline with the cable & battery post with it set to the Amp scale. The value should be below 35mA after waiting for at least 15 minutes with all doors closed. If it is not, then one or more items in the truck are remaining powered up. You can then reconnect the battery and move to the fuse box. Remove each fuse and repeat the test with the multimeter.

 

Never disconnect cable when running or you could be buying a new computer or something else.
Take Blazer to Autozone and test your systems for free.
It was ok in the days of generators to disconnect cable about 50 years ago!