|Which end of the data cable you connect first is not going to make any difference. If you saw a perceived difference I would chalk it up to chance.|
You didn't state where you are looking for the external. If the external is not partitioned it probably won't appear in My Computer. Try looking in Disk Management.
Also, if you are connecting to a USB port that is sharing a controller with a high current draw device that may cause an overload condition and the external will not be connected.
If the external is a USB powered 2.5" model that is more likely. AC powered units are preferable for that reason. Many USB powered units come with a Y cable or 2 cable to connect to 2 USB ports for that reason.