I know this isn't LS1 related, but I bet this problem can be solved in context of thinking about an LS1.
My little brother was driving his LT1 this morning and he said he was just rocking out with the radio on, then suddenly heard a loud pop from the motor and now it's totally dead. It will turn but makes a funky noise, but definitely won't attempt to start.
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Could be a timing chain. Check compression. If it's the timing chain, you'll have little or no compression. The loud pop might have been a backfire, which is typical when a timing chain fails. To diagnose a timing chain in the old days, we used to pop the distributor cap and check to see if the rotor was turning during cranking and that timing was correct. That's pretty hard to do on that front-mounted LT1 distributor!
Good luck! The timing chain looks like a pain in the butt on the LT1.
If it is broke though, you have some serious problems.
When my cam timing gear on my 94Z let go, I bent all the intake valves. Mine made a funny noise and then stopped working... it would crank, but not start. If you pull the valve cover and some of the rockers are very loose, and/or the valves are at different heights with the rocker arms removed, that's bad.
Yeah, you could remove a valve cover, crank the engine, and see if the valves move. But if the timing chain has just jumped a tooth, everything may appear to be OK. To me, it would be easier to just pull an easy spark plug or two and check compression. The readings will be non-existant or VERY low if there's a timing chain problem. It is a more positive test and, to me, it's easier.
I don't know if the LT1 is an interference motor in stock form. In an interference motor, the valves travel into the area that the pistons occupy at TDC. As Camaroholic alluded to, an interference engine will often bend the valves if the timing chain lets go - that's when you'd see the valves at different heights with the rockers removed. Most pushrod engines are not interference engines in stock form, but, if you've got an aftermarket camshaft or high-ratio rocker arms, you'll likely have a problem.
Since you've already been cranking the motor, any valve bending is probably already done. A compression test shouldn't hurt anything. If it indicates a problem, then pull your valve covers and rocker arms to see if the valves are bent.