If TowerFall Ascension for PC will not launch, please try the following...
TowerFall Ascension for Steam can only be launched through the Steam client. If you do not have an internet connection, Steam's offline mode should work fine!
To do this, right-click TowerFall Ascension in your Library.
Select Properties, then go to the Local Files tab.
Select 'Verify Integrity of Game Cache'
You may also need to manually run some installers required by the game to make sure everything was installed smoothly.
Exit Steam entirely.
Browse to your TowerFall Ascension installation folder (usually C:\Program Files\Steam\steamapps\common\TowerFall\)
Run the following installers:
Reboot your computer and test any issues again.
You can view the minimum requirements of TowerFall Ascension on its Steam page. In particular, make sure your operating system supports DirectX 10 (Windows XP does not, and neither do some Virtual Machines).
Send Matt an email at: mattmakesgames.help@gmail.com
Please keep in mind that I am only one person, but I'll do my best to help you if you've already tried the above solutions!
It's possible that someone else has had the same problem and solved it already. TowerFall's Steam community forums are a good place to check for this. If you have a problem and figure out a solution to it, consider making a post on the forums to help others out in the future :)