No crank start, would push start, new battery and has power

[Batmobile]

1991 Passat Wagon 5 speed. My problem: I have been driving the car around today and parked it for about an hour. I came back to start and all the engine would do is crank over. Read on before you conclude. I've checked the fuses and relays and they all check out. What I don't understand is how I can push the car and get it to start that way and the battery is new so the car will crank and I get panel lights. Are there fuseable links or another fuse block besides the one on the driver's knee board or by the battery? Time is of the essence so any help or leads to a solution would be appreciated.