I don't know who created the site or what tools they used, but you aren't the first person to complain. That being said, I have used several programs that began as trial versions, and they all ask, as the first question, whether I want to try it out for free (hit the Try button) or buy (enter a serial number). It's the same program either way, but the serial number unlocks the program from the trial mode, which will time out after a certain period (like 30 days, for example).
I bought CS3 as a download, but that was a few years ago, so I don't remember exactly what the procedure was. Most programs will take you to a purchase page, where you enter your personal and billing information, and they send you a serial number via email. When you launch the program, you just copy the SN from the email and paste it into the field. I imagine you can take as much time to complete the billing part as you are allowed by the trial period, so if it works in trial mode, it's not a deal-killer problem like you would have if the program wasn't fully functional. And I'm just guessing here, but maybe the 12-24 hour bit is the time between you submitting your info and it being verified, which triggers the sending of the SN to your email. Still, I feel for you, but that's about all I can do.