Interesting. I’m new here, so I can’t really help. Back in the old days (LoL) before fuel injection, this would not have caused any trouble at all. For other non-start issues, you’d spray some Qucik Start (ether) down into the carb, and it would fire right up. I can’t really advise that for your 2zz because I’m still learning about what works and what doesn’t with my own Celica GT.
When you say it won’t start, can you be more specific? Is it cranking, but just won’t turn over? Is it trying to start? Sputtering?