The power for the passenger side switch comes from the driver's side master switch (it's how the passenger window lockout, the square button, works). It's most likely that your switches are too corroded internally for any solid electrical connection to me made... pretty common and I'd start with that first. If you think you can tear it apart and clean it up yourself, go for it, you only need patience, a philip screwdriver, a small jeweler's screwdriver and some very fine sand paper. If you're uncomfortable with the prospect, pay someone who has done it to do it for ya.
Other possibilities would be the window control relays (one module in the drive's side door) or faulty wiring.
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