Can the Element be towed in this situation? Underlying this is a total problem of new battery but no power anywhere in the car. Perhaps lack of power is is locking the shift. I tried the shift release, but with no power to the ignition, nothing worked.
If I have to, should it be towed on a flatbed? Will the wheels even move with the shift in this position?
First off - are any of the fuses burned out under the hood? Do you have any idea WHY there's no power? It might be possible to pull the trim off around the shift lever and disconnect it. A good tow driver might have an idea there, but... See below.
Every time I've seen this come up in the past, the impound drivers are marvels at squirming underneath the vehicle and disconnecting the shift lever from the trans. Frankly, I don't know how they do it except that every driver I've ever seen either was built like a beanpole or - being forewarned, they brought an assistant along who was. Usually, it's just a matter of getting the vehicle up on to a flatbed.
The alternative is to stick a dolly under the rear wheels while the front lays in the cradle. Of course, if it's a regular impound and they don't feel like it, they'll just cradle one set of wheels and let the other set chew on circumstances until it's resolved.
With the rising percentage of all wheel drive cars, it happens a lot and they're used to it. I don't know how far you could go before the clutches in the rear axle burn up in a Honda but I doubt it's very far.