How to fix a Shimano STI shifter that won't shift

This is the process I typically use when freeing up a sticky STI shifter that won't engage to shift the gears. This issue typically happens on shifters more than a few years old, that maybe haven't been in use for a while and/or been exposed to the temperature changes you would normally find in a garage or storage shed. Over time, the lubricant used in the shifting mechanism can thicken up, get gummy and cause the internals to stick in place and malfunction.
This video demonstrates a quick flush method that requires no disassembly and generally works. If this method doesn't solve the issue after repeating a couple of times, the shifters can be removed and soaked in boiling water, an ultrasonic cleaner or soaked in a more powerful solvent.
As a preventative measure, it's a good idea to occasionally lube the shifters with your favorite wet lube when doing normal maintenance on the bike.
I made a similar video for rapid fire shimano shifters that has a better visual on the pawl mechanisms that typically stick. They're very similar to the mechanism in STI road shifters for reference. The video link is at the end on the end screen.
Another video is on the end screen demonstrating other possible shifting problems associated with these shifters.
Link to finish line lube I like to use: https://amzn.to/2pFLDEU