I am happy to report that the project was completed successfully. Thanks to everyone's advice. This is what I have done:
Imported some new photos, directing them to be stored in a subfolder created in the new external hard drive G:. This folder, namely "My LR Photos", is intended to store all my photos in LR from now on. I figured this will force the G: drive to appear on the folder panel of my LR. It did.
Next, within the LR on the folder panel, I moved each photo subfolder from C: drive to the new folder in G:. All photos moved smoothly with their previously established data intact. None has to be reconnected to its original.
I relaunch LR several times to make sure it works and got no problem at all. It even seems to work faster now too.
I'd like to thank all three of you for taking the interest in sharing your knowledge and helping me to do this so painlessly. Best regards.
Special note to JimHess: I really appreciate your conversation with dj_paige helping air cake2 with his/her problem on another thread. I had an almost the same problem with my LR and worked it out nicely based on yours and dj's information to air cake2.