I picked this printer up with a bunch of filament for $60. The build plate was really loose so I took it apart and found that the bearings are loose within the plastic part. Not really sure what to do here. I might epoxy the bearings in place. I saw that there is a y axis linear rail upgrade for $40 but that seems like a waste of money.
Try to somehow fix it in place, shim it for example. See if that works for now. When you got the printer printing at least a little, print a replacement part.