I was able to follow the instructions in the following video, although I used a clear aftershave splash from Gillette instead of 90% pure alcohol cleaning solution. The splash is also alcohol (percentage unknown) and it was the closest alternative within my arm's reach.
It fixed the problem temporarily, and I was determined not to touch the power button. But the next day I pressed the power button out of habit to turn the screen off (oh, don't we all love it when habits work against your willpower). Sure enough, the button jammed again and the phone went in to boot loops.
I was able to shake and hammer the phone on my hand to unstuck the power button again (if that doesn't work, try the above video again; but I was at work and didn't have access to the tools). The problem now turned out to be that I cannot turn the phone on without touching the power button. To do this, I looked up and found a very simple, clean and neat solution here in this video (other solutions involved entering some sort of download mode, installing some empty installation and rebooting etc... too much work and definitely not amateur-friendly!):
In this method, all you needed to do is unplug the charging cable, pull out the battery and put it back in really quickly (before the phone shuts down completely) to shock it into booting up. This worked and I was able to boot up my phone.
Finally, a minor problem is how I can turn off the screen without touching the power button. While I can simply wait for the screen to time out, it didn't seem elegant, especially when I'm in a hurry and can't wait. For this reason, I found an excellent app (over 5 million download and 4.1 rating from 92K users):
I installed the app and it added two icons. In first time set-up you have to allow it to become a device administrator with the permission to control screen locking (nothing else). This allows the app to turn the screen off. Normally you would "launch" one of the two icons to turn the screen off (you can add this app to your home screen as a shortcut). But I also got in to the settings of the app (using the other icon) and turned on the "Enable shortcut in notification area" option. This added a persistent notification in the panel so that I can quickly turn the screen off without going to the home screen.
Now, I just need to kick my habit for good and boost my willpower to avoid touching the power button. At least till I get around to getting a proper repair job done on it.