Formatted MBP. Can't install Mavericks
Did you format your whole drive, or just the Data Partition (usually called Macintosh HD)

If you formatted your whole drive, holding down Command+R will take you to Internet Recovery (if your Mac has either had the EFI Firmware Upgrade for Internet Recovery or it's pre-installed on a relatively new Mac), or else do nothing, and flash a ? mark, indicating that there is no bootable partition on any available drives.

Internet Recovery doesn't work on captive-networks, as you've discovered.

I suggest you take your Mac to an Apple Store, use the Free Wi-Fi to connect to Internet Recovery (if possible), and download your OS from there. 

If Internet Recovery is not a possibility, then I suggest you make an appointment with an Apple Genius, and he/she should be able to guide you through the steps necessary to re-install OS X Mavericks.