Bad luck! It does sound like your ps pump has failed again as I believe all the control circuits are within the pump itself......did it come with any used guarantees? The pumps are rarely worth fitting secondhand unless you can be sure it is very low mileage or recently reconditioned. Most new or recon pumps come with a 2 year guarantee.
The electronic control circuit components inside the pump have probably failed due to heat or a build up of conductive graphite dust inside from the motor brushes. They sometimes work again if you strip the pump and clean out inside using the various guides posted on the Mini forums (see below)......however this is not always a total fix and you may have to repeat the job if you do try this. Power Steering Pump replacement - Forums
Don't allow the pump to run flat out non stop for any length of time as they can badly overheat, causing very hot power steering fluid to damage the steering rack internal rubber seals.