I would say: Erst habe ich nichts gefangen, wollte schon aufgeben. I would avoid the "hab'" which is quite colloquial in German. The normal form is "habe". An alternative is: Zuerst habe ich nichts gefangen und wollte schon aufgaben. I hope this helps.

Google translates it as "At first I did not catch anything, I wanted to give up" (after correcting the spelling of "shon" into "schon"), which is absolutely ok. What's your problem with this?

I don't think Google's translation is that bad – what's your problem with it?