The problem is almost certainly a clog, but not where you're thinking. After the front filter, there's an air chamber before the motor that constantly accumulates dust - that's where most of the stuff gets stuck. Remove the rear grille (usually with two or three screws) and run a damp cloth inside it, then blow carefully. This fixes it most of the time.
If it's still weak after that, the internal air duct might be clogged too. Some Philco models have a plastic tube inside that collects lint. Try running a thin wire or a vacuum tube through the inside of the hair dryer (with it unplugged, of course). Just be careful not to damage anything - go slowly, don't force it.
A burning motor would be much more obvious: you'd smell something burning, the device would get too hot to hold or it would just shut off. Weak like this is a sure sign of a clog, and these get fixed with cleaning. If it still doesn't improve after all this, then it's worth taking to a technician because it could be something internal with the fan.