If the timing belt broke while the engine was running there's a really good chance your engine is toast. The VG engines are interference engines, which means that when the timing belt breaks, the cylinders smash into the valves, causing big issues.
This article gives a full description of what I mean.
There's a slim possibility that nothing was harmed, so in the event you've already verified you're good to go, I have a few other thoughts.
If the engine starts and runs fine with the throttle pushed, it's probably an issue with the IACV (idle air control valve). Do you notice it's harder to start when it's warm vs. cold or vice versa? Is it throwing any codes?