I have a PowerShell script (that works). In Windows Task Scheduler I created a new task to execute \"C:\\Windows\\System32\\WindowsPowerShell\\v1.0\\powershell.exe\">
I've done this before and had similar issues. It's almost always the PowerShell security settings. Most obviously, I would double-check your execution policy (assuming that you've set it).
Which user does the task run as? Has that user run a PowerShell script before? If I remember right, each user is prompted to "allow" PowerShell scripts to run (Y/N), when running a script for the first time (regardless of execution policy). That has bitten me before. Try:
After the first run, you shouldn't have to worry about that again, and it should run from the task scheduler just fine.
Depending on your domain security, you might also have to set the group execution policy. Here's an article that details how to do that, as well as a couple other things to check: PowerShell Security.