Sorry, but you the only way to get consistent downloading off rapidshare to to pay the monthly fee, as you can wait for a download free slot, but sometimes they ban your IP for a whole day, so you have to go back the next day to download more parts of your file.
That's new to me. I download some volleyball matches from rapidshare, and it's really nothing like you say :)
You choose a link with file, then the option "free download" (no need for a Premium User paid account) and wait about 90 seconds, put in a code (4 characters - letters and digits), if you're lucky and they're having happy Hour you don't even have to wait those 90 seconds.
After the file is downloaded, you need to change your IP address, for me it's quite easy, I re-start the router and I can download the next file. Only sometimes the new IP is too close to the previous, so you have to repeat the process.