We isntalled a new battery in a '93 probe--and it won't start, but everything is getting power. How do we start it?

We've had a very cold winter here in the Rockies and had to replace our cheap battery with another one. We know there's some sequence to get the car to start (related to the anti-theft system), but we tried everything. Suggestions? (Last time a Goodyear dealer had to do and wouldn't tell us--we even have the pink slip--my wife's owned this car since it was new.)