First thing you need to do is make sure that all of the blind slats are in the correct position. Sometimes an alignment issue can prevent the blinds from closing properly, and simply adjusting the slats can fix the problem. You don't want to force the slats into position, as this can often lead to a breakage. Instead take the misaligned slat between your fingers and one slat at a time, rotate them back into the correct position. You should be able to just flip the slat over, so it is still sitting on the blind cord but is now upside down. Repeat this process on any slats in the wrong position, and then try to tilt the slats again to see if this fixes the issue.
If you have adjusted individual blind slats and the blind still won't rotate then you will need to take a look at the blind mechanism. On occasion there might be a blockage, such as a build up of dust that is clogging up the mechanism. So first check the mechanism to see if there is any obvious blockages or pieces of debris that might be causing an issue. Should everything look as expected, then the mechanism might just need lubricating. If the blind is opened and closed frequently then it just might have gone a little stiff, and will just need some WD-40 to loosen up any cogs or moving parts that might have seized up. Spray parts of the blind mechanism that have interlocking or connecting parts - such as rotating parts, or cogs and wheels that are likely to move. You may also wish to look inside the headrail and spray a little WD-40 onto any joints which connect the rotating metal rod to either side of the blind.
Once complete you should slowly tilt the blind open and closed, and repeat this process for several minutes. This should allow the lubricant to spread throughout the blind mechanism, and reach areas that were not immediately visible or accessible. If sprayed in the right areas then this should loosen the moving parts of the blind mechanism, and then the blind should be able to tilt with ease.
As with tilting issues you should check that the blind has no obvious errors, such as misaligned slats or knots or tangles in the blind cord. You should also check that the cords are clean, and that there is no dust or blockages causing a problem with the mechanism. If there is no obvious issues then you should attempt to gently close the blind. It is important that you don't force the blind open, as if the blind is jammed then yanking on the cord could pull the blind out of its brackets, or pull the brackets from the wall.
So if the blind isn't opening then don't try to force it, as this can cause more damage. Attempt to lift the blind slats by hand, taking the blinds with both hands and lifting them so that you are holding a bunch of slats, and are taking the weight off the blind mechanism. Relieving the strain on the mechanism, might be enough to free up the mechanism and enable it to work properly. Lift the slats as high as you can, trying to get them as high as the headrail. Then try to pull the blind cord to see if it moves freely, now that the weight of the slats has been removed. Keep in mind that you might have to angle the cord just right, as it doesn't pull straight down, but rather at a slight angle to the right or left. By doing this the cord lock should be released.
If you are still having difficulty then lower the slats, letting the blinds support their weight again. Then you will need to locate the locking mechanism, and make a slight adjustment. It will be located inside the headrail, usually on the same side as the blind cord is located. Once located you should see a component that can be adjusted using a flathead screwdriver. Place the screwdriver against the mechanism and softy push, this should disengage the lock and force the blind to close. Be careful when doing this, as if the slats all drop at once then this can cause damage.
So it is better to take the weight of the slats yourself, and once the locking mechanism is disengaged, allow the blinds to lower slowly. Once the blind is fully closed then it might be worth applying some lubricant (such as WD-40) to the locking mechanism to ensure it doesn't seize up again. Now that the blind is in the closed position you should try to open the blind slightly, using the cord. Then go ahead and close the blind. Repeat this process several times to ensure that the cord is working correctly and that the locking mechanism operates are required. Once you are happy that the mechanism is working properly you can open the blind fully, and try to close it again. Hopefully the blind should now work as expected. If you are still having issues then the locking mechanism may be faulty, and you may need to replace it. Luckily these are inexpensive, so you can fix the problem quite cheaply without the need to replace the blind in full.