I'm a first-time filer and my parents claimed me as a dependent last year, so I put in $0 for my 2016 AGI, but the IRS rejected that number. What should I input?

The zero is correct.  

Try submitting again.  If you get the same error, print the return and mail it in.

Sometimes, returns continue to get rejected even though there's nothing wrong with them (data mismatches, dependents already claimed, and so forth).