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The washer sticks on 1 minute when it can't balance the load so it keeps trying to balance the cycle before it finally spins. It sounds like it just keeps trying to balance the cycle over and over which is why the clothes come out soaked and never spun out. First, make sure whatever you're washing can be balanced. Bed sheets, pillows, rug etc will usually never balance and that isn't a problem with your washer--you just need to bring them to a laundry mat or air dry them.
Now if it won't spin even with socks and shirts or nothing inside at all, open the door and spin the basket and make sure it spin smoothly. If not, then the bearing on the back could be going bad which will cause the washer to not spin because it thinks the load is out of balance. If the basket spins smoothly, then you need to replace the motor because there is a tachometer built into the motor which tells the washer whether the load is balanced or not and it's apparently sending a bad signal.
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