If you are using a relatively easy-to-navigate system like Gmail with keyboard shortcuts, I would recommend making a “Follow Up” folder and zipping through your inbox. Anything that looks really important at first glance (preferably based on the subject line) goes in there (odds are pretty good this will only be about 10% of the messages) and the rest are deleted/archived.
Then take an hour or two to read the messages in your Follow Up folder and respond to those that need a response (again, odds are pretty good that this will be a small percentage). It can be worth investing a little time in this process but if the thought of even doing that makes your stomach turn I’d just delete and start fresh (I’ve done this, too). I find that I worry too much if I just delete, so even doing a super quick spin through the backlog prevents any serious heartburn and catches most vital stuff.