I would seriously like to know if I am a veteran.

I did my Basic Training and my AIT in 1992 and I came home. Went to my unit for a few months then I couldn't to do it anymore and got depressed and couldn't do it anymore emotionally. I gave back the bonus that they gave me for enlisting for the 8 years and they gave me an Honorable discharge in 2000.

The thing I would like to know is if I can apply for any benefits from this.

Probably. But it would depend on the specific benefits you are seeking.

There are many definitions for "veteran" of the military in the U.S. The following is the U.S. Census Bureau definition from Veterans - Definitions and Concepts - People and Households - U.S. Census Bureau :
"Who are veterans?
Veterans are men and women who have served (even for a short time), but are not currently serving, on active duty in the U.S. Army, Navy, Air Force, Marine Corps, or the Coast Guard, or who served in the U.S. Merchant Marine during World War II. People who served in the National Guard or Reserves are classified as veterans only if they were ever called or ordered to active duty, not counting the 4-6 months for initial training or yearly summer camps.
While it is possible for 17 year olds to be veterans of the Armed Forces, ACS data products are restricted to the population 18 years and older. "

I m a U.S. Navy veteran and had forgotten that part about reservists in the above definition, and also repeated on the Vet. Admin. website (below). I know a few reservists who would take umbrage at that definition, but if you look around you will probably find one that includes reservists who were never called up to active duty.

But anyhow, you are a veteran based on the Census Bureau definition, and since you served on active duty for a period after basic training, you most likely meet most veteran definitions. Sounds like you were put in a reserve unit (possibly even without your knowledge) since they waited the 8 years before issuing the discharge. Do you have a DD 214?

From Health Benefits :: Veteran Eligibility : "Most Veterans who enlisted after September 7, 1980, or entered active duty after October 16, 1981, must have served 24 continuous months or the full period for which they were called to active duty in order to be eligible." Accent on most.

This calculator may help you determine your eligibility also: Health Benefits Explorer - Military Service Questions

There is also a financial calculator available, to determine if your assets affect your eligibility. But there are also provisions for primarily health benefits for indigent veterans, which may override all other requirements.

Finally, all American Legion Posts have liaison officers who assist veterans with Vet. Admin. issues. This would be a good resource especially if you are pursuing a "service connected" medical or mental disability claim.

Edit: You also appear to be eligible for American Legion membership, Join the Legion | The American Legion

Yes, he is eligible for American Legion, ** I am a proud life member. Just no chapters where I live (LOL)

The difference benefits will require various months or years of active duty. I doubt there are many benefits you can get, so that will depend