I wanted to ask a question about my dad's 99 suburban that won't start, I figured what better place than forum full of GM connoisseurs

Most other car forums have a section to talk about non-camaro related stuff, is it too early to start one mods?
As to the actual question. My dad's 99 5.7 L suburban was stored away all winter. When he tried to turn on last week, he noticed the alternator pulley was seized so we replaced the alternator and belt. He said it wouldn't turn on it first, but he came back a few hours later and it started right up and was running great like she always has, no misfires, no CEL. He tried turning it on the next morning and it would not turn on again, basically it turns on intermittently, but it runs fine when it does. What should we check out next?