After a great deal of problems, I managed to sort the external HD to work with my computer instead of against it.
My External is a Model - ST310005-FDA2E1-RK a 1 TB capacity.
I am running XP with SP3, on a 200Gb HD, 1 Gig Ram, 2400 CPU on an ASUS mobo and CPU.
I too run into problems with a lock up until it was warm, cold starts were a nightmare.
How I resolved mine.
Install fully as per the software within the HD itself, supplied when purchasing.
Disconnect as per "Safely Remove Hardware"
Pull out USB connection.
Turn off power at the wall to External HD.
Using a good Registry Cleaning Program (I used JV16), uninstall of Seagate Manager and anything else in the system of your computer.
Using a Registry Cleaner, go to Startup and again select everything related to Seagate, and ask it NOT to load up on Startup.
Using a Registry Cleaner, clean all remnants of Seagate software.
Once this is done, and you should still have no connection of the External HD to the power in the wall, or to your computer, Rebbot so the computer can note the changes.
From now on, you should be able to boot up in the morning from cold, and instead of automatically backing everything up, do it manually by a drag and drop method. Slow it may be, but just as precise.
Is it the computer fault or a Seagate fault? in fact you could say neither.
Seagate offer a great external HD and I have one internal of 20Gb on an old machine and it has been a dream and it is years old.
Just because the internal software of Seagate does not work as expected, does not make this product useless, there are ways around it.
Imagine if you will, Seagate making software for installation on so many brand computers, then on those you have so many varying OS's. Quite an impossible task I would say.
Seagate with XP SP3 makes it better as Windows has USB 2.0 and it takes over the recognition and it is in fact viewed by you computer similarly to a partition on the main HD.
I believe this will work on any machine, if you just let Windows do it's job. 
