>The idea here is to temporarily expose my web pages located in my PC to the internet while fixing the problem with my web hosting company particularly the database accessibility. I will let my PC online for 24 hours. Is this possible?

Maybe....
You mention database accessibility so I assume these aren't pure HTML pages and that you have IIS on your machine?
If that's the case you may be able to configure your router to redirect port 21 to your IIS server.
Users would also have to access the site using the IP address - and if that is not a fixed address then the solution isn't really viable (though there are some organisations that offer a free domain name to IP address mapping service - no-ip.com is one)..

HTH,
Viv