The troubble with copying Calibre to the new PC is that most software are rather finky about where there data files are and get rather upset if they do not place them there themselves. The way that I advise people to acomplish this is via PCMover
http://www.laplink.com/pcmover/. Once the software is moved to the new PC it will not know that anything has been done to it and work like nothing ever happened to it. You will need to move all of your data files and eletronic books, leave behind all of those settings and operating system files - the new PC will need its own not the older ones.
I also advise people when using electronic books to buy an external hard drive and keep all of your electronic books on the external drive so if this sort of thing happends to you again and you need to repalce the PC all you do is to plug in the drive.