I am new ,.. both in this forum and to Mac world. And I desperately need help!

I bought my new 24" imac just 2 months back together with Seagate FreeAgent Pro 1Tb, I connect them using firewire.

Everything was working fine until about a week ago when my Mac frequently shuts down and prompted me to press the On/Off button for a few second and restart my mac.

Initially, I thought it was my Mac, but whenever I unplug my external drive, everything works well, no more shut downs.

But today, I brought the HHD to a friend's imac, also running on OSX10.5, everything is fine, no shut down whatsoever.

I am truly confused, what's wrong???