Did Jimi Hendrix really only perform for 4 years and that’s it?

No, that's only the time he was very well known. He was performing well before that.

From what I found, he was active for 7 tears.

It's all about promotion and how well the entertainer is marketed. Woodstock solidified just about all musicians who appeared on this massive, musical, and political platform. In Hendrix' case, promoting African Americans was a priority then as it is now.  
Here's a rare interview with Hendrix on the Dick Cavett Show: https://www.youtube.com/watch?v=VGf9PTYyJ4A

Most musicians who died at 27 had a obvious short career.

He was noticed in 1967 at the Monterray Pop Festival (I think) and he died in 1971 so that's four years.

He only lived for 27 years so yes, his career was TOO brief.  I often try to imagine the music he would have put out over the years had he lived longer.  I also think he would have LOVED Yngwie Malmsteen.  I wish he could have lived to see him.  

Sometimes it doesn't take a long time to have a big influence.  That deaf dumb and blind kid, sure can play a mean pinball (I believe that Pinball Wizard was written about Hendrix).