"Triggering" a Method in C#/ASP.NET on a certain Condition to modify the Database

There's basically two options here.

Best is if you either own the server or are permitted to run a service or cron job (sorry, scheduled process ;) ) on it. Set the service up to check once an hour for anyone whose birthday tripped in the last hour, and send you a PM (i.e. write to a database table), or, equivalently, have the process which gets spawned every hour do that.

If you can't do that, and you can't persuade your host to let you do so, you can indeed check inside every request and do this sort of processing. For example my HTTP server class checks for session timeouts every request. This sort of processing needs to be very lightweight – a check before executing anything whether you did it this hour already.

Actually, thinking about it, an ASP.net web application runs in a persistent process. So you could potentially spawn a thread in App_Load which performed the same job as the service (though you will need to keep synchronisation issues in mind if you do that – but you should already be thread-safe as web requests are processed in parallel). That seems like not a very robust solution though, because there is no guarantee that IIS will keep your website in a single process indefinitely.