There is a solution. You can reasonably assume that emails more than a few months old probably no longer need your attention. There is a way to bulk delete or archive all emails in Gmail before a certain date. Follow these instructions from PC World - you can decide on the date, but archiving the emails rather than deleting them is advisable since they are still searchable by Gmail.
Okay, you've now got a few dozen to a few hundred emails in your inbox and there's no choice but to manually go through them. You'll find most can be be quickly archived leaving a small subset that still require your attention. Also, whilst you're doing this every time you delete a mail ask yourself "Is this a mail I always delete without reading"; a newsletter from a gym you no longer attend or an online store you once used perhaps. Take the time to unsubscribe before you delete; this will save you time in the long run. Ruthlessly unsubscribe yourself from mailing lists you are no longer interested in or never joined in the first place.
Now you've got your inbox down to just a handful of emails and nirvana is in sight. It is now time to change your relationship with your email so you control it. A colleague, Barry Smyth, recently published on his blog A 10-Step Plan for Productive Email. I recommend adopting most of these steps as appropriate to you. Good luck, and I hope you reach email nirvana.