You can get to the serial port pretty easily from VB6, but you have to enable the "Mscomm6" plugin somewhere in the menus (Google will show you the way). Either way, it adds an object that looks like a little phone which you drag onto your form like anything else. Then, in code, there's an event that goes off whenever a packet arrives (it works the same as a click event).
You'll probably have to hard-code the packet structure into the PIC. This is really easy, though, as all you need is one stop bit (I've done it with 9 flip flops and an op amp). Of course, the port has lots more features that you can take advantage of as well. Again, doing a google search for "EIA232" will provide all the specifics.