You should know the date by which your work visa was cancelled by your previous company. The date of cancellation will be the start of your 2-year ban.

If by chance your company did not apply for the cancellation of your work visa while it is still valid, therefore the start of your 2-year ban will start on the expiry of your work visa or your Qatar ID.

There is DEFINITELY no need for a NOC if you have completed the 2-years.