The computer was sold to you by Aldi and was "fit for use" you used it for a while before it failed.
Medion have honoured their guarantee by replacing the failed part, unfortunately another part has failed but again Medion will replace and are therefore again honouring their guarantee.
You would expect then to give you a "reasonable service" but you also need to give them a reasonable length of time to undertake the repair.
I don't think a week is unreasonable, however if you have not heard anything by the end of the second week then it is reasonable to be a little more forceful in asking exactly when it will be repaired.
You are likely to be better off being firm and reasonable rather than demanding and confrontationable.
I think you have ben very unlucky to have two failures with a Medion as they are very good machines.