Comment count in backend is wrong

Have you tried:
– deactivating ALL (yes all) plugins temporarily to see if this resolves the problem (plugin functions can interfere). If this works, re-activate them individually (one-by-one) to find the problematic plugin(s).
– resetting the plugins folder by FTP. Sometimes, an apparently inactive plugin can still cause problems. Also remember to deactivate any plugins in the mu-plugins folder (if you have created such folder). The easiest way is to rename that folder to mu-plugins-old.
– switching to the unedited default Theme (Twenty Sixteen, etc.) for a moment using the WP dashboard to rule out any theme-specific issue (theme functions can interfere like plugins).