Error message

In the recent past some plugins triggered that message. Along with recommendations above try deactivating all plugins to see if this resolves the problem. If this works, re-activate the plugins one by one until you find the problematic plugin(s).

The only plugin I see is wp-super cache and it is not fully installed.

One more thing. Change your theme to the default theme and see if Jetpack works.

Yes.

Normally Jetpack works really well so this is strange. Try their support forum, https://wordpress.org/support/plugin/jetpack and I know of no alternatives for that plugin.