How do I fix GUI Miner stuck at connecting?
you're using api2.bitcoincz.com:8332 but that's not listed on the pool's site:

Run your own GPU/FPGA/ASIC miner with the worker credentials you gave earlier, and connect it to following URL:

http://api.bitcoin.cz:8332
(Main pool URL) 

or
stratum.bitcoin.cz:3333
(If you have Stratum-compatible miner)