VoiceAttack is not, 'fighting' for your microphone. When you start up VoiceAttack, an instance of the Windows speech engine is created. The speech engine is simply listening on the device you have set up as your default recording device in Windows. Make sure to look over this thread to make sure you've got this set up to the right device:
https://forum.voiceattack.com/smf/index.php?topic=63.0 That doesn't go into using third-party apps used to route audio (not sure if you are or not). Unless you've chosen to set this value on startup (Options > Audio > 'Set default multimedia recording device'), VoiceAttack doesn't do anything other than instantiate a speech engine (which then listens to the device).
Something to try after verifying your mic is the right device is going into VoiceAttack, going to Options > Recognition tab. Click on the, 'Utilities' button. Then click on, 'Sound Settings'. This will bring up Windows' settings. On the right, click, 'Sound Control Panel'. On the sound control panel, go to the recording tab. On that tab, locate your selected microphone and double-click its icon. This will bring up the properties for that device. Go to the advanced tab and set the, 'Allow applications to take exclusive control of this device' to UNCHECKED. Click OK all the way back and close settings. Close DCS and VA and restart both. See if that helps at all.
I'm also not sure how running VoiceAttack with or without Vaicom is preventing DCS from running - If this is the case, you are the first to report it. Have you tried running VoiceAttack with Vaicom turned off and not using the Vaicom profile to see what happens? That would mean going into Options > General and unchecking the, 'Enable Plugin Support' box and restarting VoiceAttack. Once restarted, that would also mean changing to a profile other than the Vaicom profile.
****EDIT - I just realized that it's been requested to turn off plugins MULTIPLE times (not including the response on the DCS forum
https://forums.eagle.ru/showthread.php?p=4318838). Consider this thread closed until this can be confirmed, as we're just wasting a huge amount of time not looking at the major points.