Hello Susan!
Welcome to the Disney Parks Moms Panel!
I think the best way to book
Disney Dining reservations is online; however, it sounds like you are having issues getting online reservations to work on your computer. I am so sorry about this, and I know your frustration is magnified to know that your top Disney Dining choices have no availability at this time.
Even if you can't secure your reservation at first, DO NOT GIVE UP! My recommendation is to call (407) WDW-DINE every day (in some cases), to snag a reservation that has just been released. Two years ago, I REALLY wanted to book
Cinderella's Royal Table for breakfast. I called every day for three weeks, and I FINALLY booked the reservation!
If you are willing to split your party, then sometimes a Disney Dining Cast Member can accommodate your family. For example, I was able to book
Tusker House Restaurant at
Disney's Animal Kingdom for seven people a few days ago because I split my family up in a group of three and a group of four. This might not be an option for you, but this is another idea.
The bottom line is that it is not impossible to book your favorite Disney Dining reservation that is currently not available! Be persistence and patient, and your Fairy Godmother just might grant your wish!
Have a MAGICAL day!
Wes