I can't imagine what you have read on the internet that would make you think a blood test for HIV was inconclusive. It is, in fact, the only test that is conclusive.
In the hospital when someone gets a needle stick from a patient who is known to have HIV, we test soon after the needle stick (within 2-3 weeks), at 3 months, and 6 months. If someone is still negative at 6 months it means there is no infection.
HIV cannot be diagnosed by symptoms. Therefore, not having a fever means nothing in relation to HIV. In fact, most infected individuals do not have a fever after the first month of coming in initial contact with the virus. Of course, not everyone who gets the infection will ever have a fever, so it tells you nothing about one's infected status.
The only way to make certain you don't have HIV is with a blood test. If you are negative 6 months after the risk, then you don't have HIV. Everyone who is sexually active should be tested at least once a year for HIV and other sexually transmitted diseases.
A blood count tells nothing about HIV. In fact it doesn't diagnose much of anything. It only tells us "something" is wrong and we have to work to find out what that "something" is.