External Drive Not Displaying at Boot

I have a Hitachi HSD2000 external hard drive (http://www.tigerdirect.com/applications/SearchTools/item-details.asp?EdpNo=5082546&CatId=4230) plugged in by USB. This drive works fine, but has a few strange problems attached to it.
a.) When I boot up my computer, the drive is not displayed in the My Computer display. I have to unplug the drive then plug it back in for it to be shown. There must be a way around this, I think too much of this may be stressful to the drive and it's inconvenient. If there was even a way to "refresh" the drive so that it was shown (without doing it physically) that'd be fine, but I'd really like to know why this is the problem. It does this with all USB ports.
b.) Since having this drive connected, when I restart or shut down my computer, it hangs. When I shut down the computer, Windows turns off but the tower remains lit up and on. Why?

 

Do other USB devices work on your computer without problems? If you connect a flash drive before starting your computer, does the computer recognize it upon startup? Have you tried different USB ports (including both front and back)? Any difference?

 

Hi Hypen,

I have experienced the same difficulty with XP but only when two devices were plugged in. Mine was an internal 15 in 1 card reader and some other device I don't remember. I do remember removeing the 15 in 1 and useing an external 6 in 1 reader. Had the same problem.