your problem doesn't have anything to do with the screws that set the upper and lower limit for your derailleur.

it sounds to me like your cable came loose from the rear derailleur, unless it was a broken cable or your shift lever is broken.

i think that,
if the problem was with the old cable breaking or coming loose, then the problem NOW would have to be that you didn't install the new cable correctly. (didn't get the cable set to the right length, or didn't attach the rear derailleur to it tightly enough.)