Getting shapefile in right projection using ArcGIS Desktop?

I have an older map that I didn't create. I'm just trying to get everything to line up on it, and having a hard time.

The data frame is in NAD_1927_UTM_Zone_12N, as are the point shapefiles (derived from a .dbf table that I had to repair the data source to) and one line shapefile. All the other data is in StatePlane (either 1927 or 1983) and that's what shows up in the layout view (aerial, roads, buildings, polygons, etc.)

I've changed the points (via right click, data, repair data source, browsing for the data and then editing "Coordinate System of Input Coordinates" to StatePlane, but that doesn't work. The point shapefiles aren't visible anywhere, even if I zoom to the layer or go to Full Extent.

When the points are in the UTM projection, they're at a ridiculous scale (1:1,000,000) and they're all in a straight line instead of spread out like the old PDF version of the map I have.

I'm trying to make some simple edits, but I can't fix the bigger issue of shapefiles not lining up.

Although I don't know if this is the problem, when I open the map I get a notice that says, "This document may contain VBA code but you don't have a VBA license." I would just assume that scripts don't run, not that that would affect projections...

Any insight would be greatly appreciated. Thanks.

edit: No, the pdf is uneditable. I did realize the XY were being mapped to the same field, which was wrong (the XY data is in northings and eastings), but correcting that didn't fix the problem. Unfortunately, whenever I try to add data, browse for projections and the like, ArcMap crashes which is an unrelated server problem. I could copy the data to my own folder but there are a lot of files and some of them are linked and from other folders and ...still of course in different projections. Although I fixed the VBA license problem, so that has nothing to do with it.

I tried doing Data Management > Projections & Transformations > Features > Project and each time (regardless of which projection I choose) the new points project exactly where they currently are. I'm currently trying suggestion #1 at the moment.