I would point out in your image CGMiner is already running. Its asking for a pool. No need for cgminer.exe at that prompt. Can use "stratum+tcp://stratum.bitcoin.cz:3333" without quotes at least if there isn't a second server or a redirect. (wrong of me)> 2nd I don't know bitcoin.cz so this may be off but usually api is only for the API like how you get stats and remote view things not for getting work.

Once you get it back running again and the instructions above should get you very close if not running. Do the following Press "s" then when settings menu comes up (assuming you are using curses) then Press "w" no need for the quotes they just set it off from other text then "Enter". This will write a config file. It will have your pool and credentials in it. It will load everytime cgminer starts. This should get you up and running quickly and easily for the long term.

Turns out slush's pool does use api for getwork. So what you had before http://api.bitcoin.cz:8332 would work if you do the following.
At the first one after no pool found put in http://api.bitcoin.cz:8332
next prompt: your user name
Next prompt: your password

As stratum is more efficient and less likely to have rejects it would likely be a far better idea since your pool supports statum and so does cgminer to use stratum. Your rejects will likely drop to 10% of what they where or lower. As an examle 1% rejects getwork is likely under .1% rejects on stratum.