At this point I have to ask some stupid questions. Are you using the same power adapter at both places? Are you using the same USB cable? Have you tried a full - not quick - format on the drive after removing the partition and recreating it?
Sorry these seem a bit lame, but at this point, I have no idea. WDTV can be a bit touchy sometimes when a drive is disconnected improperly and I have had a problem with a brand new Passport drive that was solved by deleting the partition and then doing a FULL format of the drive. Outside of that, you may want to try another drive… There is always the (very very very slim) possibility that the drive is defective in some way.