I Don't actually think that the days of the desktop are over. On the other hand, I do think the desktop really is less relevant than the web.
The reason I feel this way is because a desktop is a computing resource, but the internet is a communication resource. Almost everything we do is about communication, whereas only a few things we do on a day to day basis (most of us, anyhow) are actually dependent on computing.
Some folks might want to take a photo, retouch some of the ugly spots, and then show it to an audience. The first step is not particularly aided by the computing resources of a desktop. Even if you have a laptop with a builtin camera, it probably doesn't take pictures anywhere near as nice as dedicated hardware like a DSLR.
The second step does benefit from a desktop. Photo retouching is a compute intensive business and the more cpu you throw at it, the easier it becomes to get good results, if for no other reason than you spend less time tapping your fingers while you apply a lens flare filter.
The last one, though, is probably the most important step in the whole process. You couldn't get there without the first two stages, but the last stage is what motivated everything that came before. And a desktop just doesn't help you with this very much, unless you like lugging around 15-30 Lbs of fragile electronics.
The real question is what are you really trying to do? Are you doing something that benefits specifically from the strengths of one technology or another? Answer this question.
On another note, I'm not sure that the answer is necessarily between .net on the desktop or PHP on the web. Can you talk your boss into allowing you to use ASP.NET? This seems like it might satisfy both of your needs. He wants it on the web, you are familiar with .net.