It's possible that the thingie at the top right is stuck in a locked position, which would keep the cords from moving the blinds. Have a look and try to wiggle it to see if that's the problem.
BTW, those probably aren't what we used to call Venetian blinds...the ones with wide slats and 1-2" fabric tapes...I have no idea what's another name for Levelors, but they are vinyl blinds with slats about an inch wide. They're very inexpensive...like just a few dollars each...and easy to install. You may be able to use the hardware that's already there and just take down the old blinds, pop in new ones.