Then I connected that to my laptop and it worked. I copied GBs of data without any issue. I knew there can be power issues for external devices when connected to USB ports. However, since my PC was working in superb condition, I never suspected that it is running without adequate power. Who suspect our own friends

I replaced the power unit with a Mercury 450W one (Bought from Digital house). I heard Mercury is better than other OEM unbranded units (even my earlier one was marked as 450W as well). After this, Seagate external hard drive started work like a charm as well. It is now coping files in lightening speed which made me happy to share this information with you.
WinSoft technical guys were really okay. When I wanted them to have a look at it by thinking there is a manufacture fault, they have given it top priority and copied GBs of data in-front of me. Some people are too lazy to do these things. So I'm really satisfied with their service and highly recommend Seagate Expansion Portable Drives. I also would like to recommend Mercury Power Units. Seems they provide the power as marked in the label.