It's a bit from Bach's Toccata and Fugue! At 2:40, after a short general break, the piece picks up with that melody.
I feel it is sampled a lot, and similar melodies have shown up a lot since it came out in the 18th century.
I wonder if you mean the Beatles' "Dig a Pony", from Let It Be!
It has the "A... Ha... A.. Ha.." effect, and the "Because".
There are clearly parts of your piece that don't match this, including parts you seem quite emphatic about, but... who knows, when taken with the effects of memory, time and imagination?
Based on information at this website Covers by JH. Could the song be
"Tax Free" by Carlson and Hansson ? "They licensed the track Tax Free to Jimi Hendrix".
I couldn't find a version with the intro you mention, but it seems a pretty good match to the other facts.
The track is on one of the compilations released after Hendrix's death, &...