I handed the parcel to UPS with a note that should be delivered on a certain day, but a week has passed since that day and I can't even track where the parcel is at this time.

It is very hard for me to believe this, because I constantly use UPS services and I have never had any problems with parcel delivery all the time. Everything was always done on time. And I strongly advise you, if this has already happened, to contact the employees of this company through the ups customer service website and I am sure that everything will be resolved in the best way.