This happened at my apartment recently. The caretaker kept claiming that the problem was the screens and that nobody else in the building was having any problems, when that clearly wasn't the case, as even the laundry room had piss-poor pressure. We had to shower with a big cup so we could rinse our hair, which was a problem because the great water pressure was one of the main reasons we chose the building we did (I take water pressure seriously). A plumber came over and emptied the screens (which I could have done and which were 99% clear) and claimed that took care of the problem. It didn't. The plumber came back and checked to make sure the pipes were turned all the way on (they were, of course), claimed that they weren't, and said that took care of the problem. It didn't. We called him again and he came over and changed some of the various gaskets and claimed that would solve everything. It didn't. He came back and changed some of the faucets, claiming again that that was that. It wasn't, of course. The water throughout the apartment was still atrocious. Just when we were about to move after a week or two, the pressure miraculously went back to previous levels. They claimed they didn't do anything, but I have to believe other people started complaining and they fixed some problem with the boiler or whatever. Not sure why the plumber kept claiming he had fixed the problem when he clearly hadn't, but oh well. Anyway, I sympathize big time. Having no water pressure makes it difficult to do many things. I wish I could offer a sure-thing fix, but all I can really say is to try some of the things the lying plumber who came out to my place tried: screens, water shut-offs (you've tried that already though), gaskets, faucets.