Originally Posted by Retro Grouch

Oh dear!

Front derailleurs are MUCH more picky about adjustment than rears. There are several adjustments and each one affects the others. Once it gets screwed up, if you don't know what you're doing, there is a tendency to pile one misadjustment on top of another in an effort to get it to work right again. Jacking with the limit screws is a sure indication that's been done. Once correctly set, limit screws never need readjustment.

My advice is to start over from the very beginning. Go to the Park Tool website. find the tutorial for installing a front derailleur. Completely disconnect the shift cable and start from the very beginning as if you were installing the derailleur for the first time. Do the steps in order and don't be tempted to skip any because each adjustment affects the subsequent adjustments.