Is it possible for HIV to lie dormant for 4 years before showing symptoms?

Yes indeed. This is exactly how HIV behaves. HIV infected people usually feel and look entirely well for up to 10 years, sometimes even longer. But the infection is not truly dormant; the virus is busy destroying the immune system. If you think you have HIV, absence of symptoms doesn't mean anything; you must be tested to know. If you are at risk and haven't been tested, do it now! Good luck.