Admiral 7010L will not always spin?

My admiral washing machine will not spin sometimes, when this happens there is a loud solenoid click but the spin cycle and pump do not start, the timer can still be heard ticking away. After switching the machine off for a few minutes the spin cycle and pump usually start to work. This morning the same happened again, after switching the machine off for a few minutes and then back on, and putting it on the spin cycle the water pump stated but the machine would not spin immediately, it started slowly at first then got faster and faster. The door switch has been checked and is working properly. Please HELP!!!!