How can I ask for compensation of my sufferings from private but reputed organisation (service provider)?

No doubt you can seek financial compensation and cost against the service provider for all sort of losses suffered by you due to their deficiency in providing services up to their commitment and standard for which you paid or promised to pay.

The formal complaint can be made against them in the District Consumer Forum and will be awarded the financial compensation/cost against them on the basis of the evidence you produce for the losses suffered due the deficiency in their services.

A prior written notice to the service providing company has to be given by you first before you file formal complaint against them in the District Consumer Forum.

The compensation/cost that is usually awarded is much lesser that you expect and spend for claiming it but the only thing of satisfaction for you will be to tell your friends around how you made a big company to bow down before you and pay you compensation/cost for their deficiencies.

Best Solution: Discontinue their services and go in for prepaid connection with another service provider, you can maintain same phone number while doing all this.