Is there a way to have my second monitor usable?

From searching Google it seems to be a problem for a number of people, and no one has any real fixes.

A few options you have: (while running in windowed mode)

• Press Ctrl-Shift-Esc bring up the task manager go to the Applications Tab, Right click on Civilization 5 and select Bring to Front. When you click back on the game again it should be over the task bar.
• As mentioned in a comment, set task bar to auto-hide.
• Run the game in windowed mode at a slightly lower resolution. This will resize everything so you can always see it.

I just do the Bring to Front option as it puts it all back and seems to only have to be done once per game run.

Try changing to Windows 7 Basic in Control Panel - Personalization. I was only able to to interact with Windows Desktop on other monitors during Civ V fullscreen using this setting. You have to change the option Bind mouse to Never in Interface Options i Civ 5.

Edit 1: I have tested some more as I have similar problem as you. If i enable full screen my two other monitors turns black, and i have to Alt+tab to get to the desktop. I think the problem lies with a feature called Desktop Composition. When enabling Windows 7 Basic theme you disable this feature. Only disabling this feature makes Civ 5 full screen and multiple monitors work for me. You can disable it in Control Panel - System - Advanced System Setting - Settings (Performance). I still have some issues when windows appear on primary monitor where Civ 5 is. I have to fetch it my clicking several times somehow, and sometimes the screens will flash black. But at least it works.

As for your specific problem i Civ 5 window mode, it seems you can just move your start menu to the other monitor.

Edit 2: Quick google on Civ 5 and desktop composition leads to http://forums.civfanatics.com/showthread.php?t=436775 which tells you can disable it on the Civ 5 exe-file in the steamfolder. This will at least turn it off when launching Civ 5 and re-enable it when game is closed.

It works with my setup (HP Pavilion Dv7 with an external 24 inch monitor) I play the game in the window mode on the 24 inch monitor and am able to use the other monitor at the same time. Occasionally I have the problem you have with the start menu being on top once in a while and that usually takes a game restart to fix the problem. The only time it does it, (not every time) is when I minimize the game window do something else on the 24 inch and them maximize the game window back.

Not an answer but a possible workaround. Try to enable "Auto-hide the taskbar" option when playing Civ 5 and maybe place it on top of the desktop (or left/right/whatever area you are less likely to hover over accidentally while playing) vs. bottom. It will dock and hide and your "taskbar above game window" issue might dissapear.