Run as a different user from SYSTEM account

You will have to use cached credentials in this case. You can run notepad from powershell with encrypted stored credentials.

Run these lines to create a cached credentials file.

<# Set and encrypt credentials to file using default method #>

$credential = Get-Credential
$credential.Password | ConvertFrom-SecureString | Set-Content c:\scripts\encrypted_password1.txt

Use the cached creds:

$username = "account"
$encrypted = Get-Content c:\scripts\encrypted_password1.txt | ConvertTo-SecureString
$credential = New-Object System.Management.Automation.PsCredential($username, $encrypted)

Start-Process notepad.exe -Credential $credential

Please store encrypted password file in a safe folder protected by NTFS permissions from viewing by other users.

Another solution is to compile script as exe file with built-in credentials. You can do this with free ps2exe powershell module.