I think your battery is still dead. You can't recharge a completely dead battery just by running the car for a little while. If you hear clicking that means the starter doesn't have enough voltage. Some little lights or the remote might work because they require very little voltage, but a starter needs massive amperage to work, hundreds of amps.
Take your battery out, have it fully charged, then load tested, and for the future, please don't ever jump start a totally, completely, dead battery--it could blow up or if it doesn't, it will really put strain on your alternator.
Since you may have crossed cables, there is also the possibility that you damaged the alternator, and hence not getting enough charge to the battery.