It could be the actual belt that drives the pump. Or a seized idler pulley. Pumps themselves do not usually makes that noise, unless the bearing in the pump is shot. Lift the bonnet/hood while engine running and in park/neutral with handbrake/park brake on. Then watch the pump pulley as it spins, have an assistant turn the wheels slightly side to side. With engine off, twist the pulley belt sideways to check flex and slack. If you can turn the belt 180 it is time for a new one. Also check the pulleys and idler pulleys with engine off by just grasping them and trying to wiggle them by rocking them back and forth in a top to bottom position. Your're checking if they will move forward and backward in either a 12/6 or 9/3 position. They should be tight in that regard.
You will need to check if there is a fault with your front and rear abs wheel sensors. Hook it up to a scanner, reset all the codes. Drive it and see what resets. Check all your wheel sensors by removing and visually inspecting the units. Wipe any grime or grease off them then replace. Check all the ABS sensor cables make sure they aren't broken or damaged in any way. Replace any suspect ones. Last of all check all your fuses.
Could be fuel, spark or air. If it is an electric fuel pump, when you first turn on the key you should hear it prime, if you don't that is more than likely your problem. Check your fuse first. If not electric, check your fuel filter and or vacuum line to the pump. Take a look at your air filter see if it is dirty. If so either clean or replace. If no joy, then move on to your spark plugs, see if they are producing a nice fat blue spark. Pull the leads off all plugs, pull out one first or all. Pop one in to the plug lead you wish to test. Ground the plug, then hit the starter. You should see a fat blue spark. If not, clean and re-gap your plugs or renew. If cleaning and re-gapping, then retest your plugs. If renewing reattach everything and run. If still nothing, look at fuel. If carburettor, see if it is gunked up and if you are comfortable with pulling it apart do so. Clean it out thoroughly. Put it back together. After all this, and still nothing. Then it could be a timing or valve clearance issue.