Just to state the obvious: something has the wrong projection/coordinate system. Have you worked with the polygon features before with other projected features, and have them line up correctly with other data? If that's the case, then rename the .prj of the points to .prj.bak; and start troubleshooting the correct projection for your points. I would guess that the points' coordinates are a bit more universal: decimal degree, WGS84, UTM, etc., but that's just a stupid guess.
The way I troubleshoot for unknown coordinates is first to start with a blank map document (remember that ArcMap sets the data frame's projection property to that of the first shapefile or feature class that's loaded into the data frame). Then load the shapefile with the renamed projection file, and look at the coodinates at the bottom of the map document window. The data frame will still have an unknown coordinate system. See if those coordinates look familiar (decimal degree, continental system, WGS84, UTM, etc.), I may get lucky. Then load a shapefile with a known good projection file that should overlay the points.
If that works, great. Define the projection with the one you know works, delete the .prj.bak file, and you're good to go. If that doesn't work, then you can try setting the data frame's p/cs property until you find one where the two shapefiles line up properly (ArcMap will automatically move the shapefile with the known good .prj to the correct location, based on the data frame's p/cs property). Then define the points' projection to the one you just found.
The problem with troubleshooting is that sometimes trouble shoots back.