If they are applications that were originally installed by drag and drop then that would be fine. If they were installed by an installer then you would likely need to use the installer once more as it may have placed files outside of the Applications folder.
Time Machine is best at restoring personal files OR a complete system.
However, I have one more thing for you to try before re-installing, it might have no effect but at this point I think its worth a shot.
1) Open System Information (under Apple icon in upper-left, click About This Mac, click More Info)
2) Click System Report button, under Hardware, find your "Model Identifier" -remember this for use in step 6.
3) Navigate to /System/Library/Extensions and locate IOPlatformPluginFamily.kext right-click and select Show Package Contents
4) Open Contents/PlugIns and locate ACPI_SMC_PlatformPlugin.kext right-click and select Show Package Contents
5) Open Contents/Resources
6) Find your MacBookAir?_?.plist (? = your model identifier from step 2) and delete the file