I understand how upsetting it would be to haul an appliance across the country and have this problem.
When the washer was moved, were shipping bolts used? If so, were the shipping bolts removed? Check to make sure washer is on a level floor and leveling legs are adjusted and secure. Is the washer unbalanced during agitation or just in the spin cycle.
. Use image below to raise washer lid to check spin basket and suspension rods. The problem could be a defective balance ring on the top of the spin basket, broken balance spring, or broken frame. The balance ring sits on the top of the spin basket and contains liquid that helps balance the spin basket. If the ring has leaked the liquid, it will shake badly.
If the problem is not obvious after checking these items, please reply with a full model number for additional help. The model number would look like 110.xxxxxx. The number provided looks like a serial number.
If you would feel more comfortable having a technician make these check, you can schedule a Sears technician here;
Sears Home Services
Thank you for using Manage My Life.