Since there are a couple of incarnations of OBJECTID columns in there, I would track down the geometry featureclass that the data originated from and perform a Join using conventional methods, or the Add Join tool from within ArcToolbox. The geometry exists somewhere... your are currently lost without it.
If you can get the original geometry as Dan indicates that would be your best option. If you just want to see an approximate location, you could geocode the PROP_LOC against some centerline data if you have it. I'm not sure what the ST_ADDRESS field contains. Sometimes it's the same as the PROP_LOC, sometimes not...
I agree with Dan and Joe. Since you have shape areas, this means you have polygons and cannot really 'plot' these on a map without some sort of coordinates. The shapes would not know what shape to draw.
You can potentially look into
There are tools in this to map your spreadsheet data. But, you still have to have some plotable features like XY, addresses, etc.
If you had spatial features that included the GIS PIN, you could build your own locator from it using the General - Gazetteer address locator style, where the place name would be mapped to the GIS PIN field. Then you could geocode the spreadsheet based on the value in the GIS PIN field to be able to place the location on a map.