Your coefficients are all enormous in magnitude suggetsingsuggesting that in fact they are tending to infinity or minus infinity. This in turn suggests that the problem is separation. For some combination of your predictors you have pefectperfect prediction. There are many posts on this site tagged separation which offer guidance. Of course if that does not help then edit your question with more details to explain what else moghtmight be happening.
Edit in response to comments by the OP
One way of exploring the issue further would be to refit the model deleting each variable in turn. So if there are currently 20 variables you would end up with 20 new models based on 19 variables. Then examine these. If the separation is due to one variable then the model without that variable will now look very different. If it is due to the linear combination of several variables then it is possible that all the the models involving those variables will now look OK. Then at least you know which variables to investigate further. Note that this is not the same as the automatic application of step-wise methods.