When did you buy it? Apparently last year there was a bad (for want of a better phrase) batch of ac (power) adapters with some medela swings. I've had a similar problem; originally I thought it might have been milk getting into the motor but have since worked out that that hasn't had an effect - tested this by using batteries in the swing and it works fine.

Try using it with batteries (the lithium batteries are good but expensive) first.

If that works, ring the place where you bought it from and they should be able to replace the power pack sometime soonish. I know that Mothersdirect are waiting on replacement power packs to send out to a number of people because of this problem (I'm one of them). Currently I'm just using my swing on batteries and it's going well, no stop, start stuff happening.