I have a 1989 Stihl 028 AV. I have had many problems with the oil pump. In one instance the dealer (this is before I had a grip on doing saw work myself) blew the lines out and said that he replaced the pump. I blindly accepted this and went on because the saw oiled better (but not much better). After several years of setting in my father's shed, I reclaimed the saw with the intent of making it oil, or making a concrete saw out of it. By this time in life, I have a friend that has opened an outdoor power equipment shop (Stihl, Snapper, Simplicity, and Ferris) so I figured I would let him take a look. We opened the saw up and, ta da, the original pump "bandaged" but worthless. All that is to say, $80 later (pump cost) I have an 028 that works better now than the day it was bought.
As side notes, the older 028 AVs do not have an oil adjustment screw...so if you don't see it, don't feel badly. If you have to take the saw in for an oiler, I would recommend picking up a round ground (easy to file), full chisel chain (if you don't have one, it makes the 028 a wood eating machine...relatively, at least).
Jon