How's the battery? Take it out and get it checked. Cars can sound horrible when trying to start with a low battery. They can make awful grinding sounds due to the starter not engaging properly.
It could also the be starter itself. This video is a Buick, but all cars are pretty much the same in how they start. They can make similar noises under the right (or wrong) circumstances.
https://www.youtube.com/watch?v=fCUglkXAoec
Always check the easiest stuff first before assuming the worst. A shop should able to check the timing chain alignment between the upper and lower pullies by just pulling the valve cover and aligning the crankshaft pulley, if you're that worried about it. Have it towed. A $50 tow is better than wrecking an engine, if it actually turns out to be a timing chain issue.
But I'd get the battery tested first. Failing that, check the starter. Or if you're convinced it's the timing chain, skip the starter and have it looked at by a mechanic before you try to start it again.