If all of your vertical blind slats are not where they should be, then your blinds will stick. If you have one slat that is crossed with another one, then the blinds will stop at the point where the two cross. To get your blinds moving again, simply put the slat that is out of place back into its rightful spot. This is a common problem that is quickly fixed.
When the metal rod track at the top of your vertical blind assembly is blocked, your blinds will stick. Sometimes pieces of the plastic clips that hold the slats in place can break off and get caught in the track, or a piece of your wooden molding could come loose and drop onto the track from above. Find the obstacle and remove it to get your blinds operational.
The chain that you use to open and close your vertical blinds runs over a plastic pulley at the top of the track assembly. Over time, two things can happen that would cause your blinds to stick. The first is that the chain has ground down the teeth of the pulley to the point where there is almost nothing for the chain to grab on to. The second issue could be that the chain has gone off the pulley. The first issue will require you to replace the pulley, while the second issue can be fixed by using a flat head screwdriver to get the chain back on the pulley.
For vertical blinds to open and close properly, the slats either need to be turned all the way open or all the way closed. If the slats are left half open, then they will bunch up at the center of the track and the blinds will get stuck. Always check that your slats are completely turned one way or the other before trying to open them.