I don't know if anyone else has had this problem, but...
I get into DosBox, watch in intro clip, and get to the menu for "New Game". Once I click the START button, I get booted back to the start-up menu. So, I can't get to the game. The same thing happens if I try to change the settings...right back to the start-up menu.
What is the solution?
Thanks in advance.

Once you click New Game, you should see a screen where you choose Galaxy Size, Difficulty, and number of opponents. Click "ok", then choose a race and a player color, a player name, and a homeworld name. Once you press Enter after naming your homeworld, gameplay begins. Where are you seeing a "start" button?

Edit: a general suggestion around here is to NOT use the default installation folder, so you may try reinstalling it outside of Program Files. Some games also require you to "Run as Administrator", which you can access by right-clicking the shortcut and selecting Properties. Last, you may need to choose a compatibility mode, also in Properties. For what it's worth I didn't have to mess with the shortcut properties for my installation, and this may not apply to DOSBox games, anyway.

Okay, now what I'm saying is that I can't get to the screen that lets me choose a race and flag color. When I get to the screen that lets me choose a galaxy size et al., any option I push, including the OK button, sends me back to the main menu, as if it restarts itself. It seems like if the DosBox stays small on the desktop, then I can use the game, but now it automatically expands to full screen.

I use the icon on my desk top, I am in administration mode, and I have the compatibility set to my operating system (win7).

Please, how do I fix this?

Have you tried the other compatibility mode options? I think I have a couple titles that I run under Win XP mode to get them to work.

And definitely choose an installation directory other than the default one. For myself, I use a second hard drive with a Game Stuff\GOG.com folder in order to keep them better organized. Something about Windows 7 and the UAC stuff can sometimes mess with the games when they're installed in Windows' Program Files folders; I'll let someone more informed on that particular issue explain all the UAC stuff with regards to these games. What I know is that you can put them just about anywhere on any of your drives (Moo1 will even run from a thumb drive) but you definitely do not want them in any of the Program Files folders.

If that doesn't fix it, then I think one of the DOSBox masters around this place can probably point you in the right direction.

When that happens to me, I deal with it by hitting ALT+ENTER once (to change the game from full screen to window) and then a second time (back to full screen). After that, the game works normally.