A whining pump can mean 2 things: 1- fluid flow is blocked and the pump is bypassing at maximum pressure, or 2- it could mean that the pump is worn internally and needs replacement. It's not easy to tell the differance between the two, and the only real test you can do is a pressure test of the PS system. Usually a shop will have to do that, since the gauge has to be good up to 2-4000 psi. Sometimes you can get an idea by cracking the pressure line banjo bolt at the rack or the pump loose, but that gets really messy really fast.
Checking for blockage involves pulling each component and checking to see if air or PS fluid moves through it(whichever is easier to test with). I would start by pulling the high pressure hose off of the rack and see if fluid comes out of the hose end (engine not running). If it does, try spinning the engine over a couple times with the starter (do not let it start), and see if the fluid flow increased. If it's flowing well, then you're looking at the spool valve or the solenoid on the rack, but that is not easy to work on or fix, and that's when most people reach for a reman rack. If it isn't flowing at all, you may have a blocked hose or a bad pump.
What I would do: check for flow through the high-pressure line by pulling it off of the rack. If it flows well, put the banjo bolt back in, but not tight. Get a oil tray/bucket/dish under the car and start the engine -for 1-2 seconds- while watching for fluid at that fitting *safety glasses!!!*- if the pump is good, it'll spray out like crazy. If that all turns out good, you are looking at a probable bad rack, and it'll need replacement. Used, part-out, reman, new, or whatever you want, but make sure it has PPS.