There are a few potential things happening here.
In answer to your specific question - The coord system is indeed EPSG:4326. The real question you're asking though is - Why is it not showing in the correct spot.
Sounds like you have another shapefile as a reference for where it should go, so that it is a good start.
Check your project settings. Under Options > CRS - check the settings there. To test properly, I would recommend setting it to 'Use a default CRS' when creating a new project. (and obviously set this to 4326). Create a new project. Load your data in.
Lets also assume for a minute that the shapefile is not reading the prj file for whatever reason. Set your setting in options > CRS - 'CRS For Layers' and set it to 'Use Project CRS'. This will make the layer project in 4326.
(If the above works, then its possible your .prj is not linked to your shapefile. (check that the names match! check for spaces. Delete it and recreate it again etc. )
If the above has not resolved the issue, then this probably means the data was captured using a different coord system. Unfortunately without knowing where you are, I can't tell you the answer. However try this.
In your local area, there will be localised map grids. Trying setting the coord system of the data to one of those local grids. Only you can work this out sorry. For instance, I live in Perth, Western Australia. The local map grid is MGA50.
You can use the http://epsg.io/ website to help you find some of these. Once you set the LAYER to this coord system, your other settings should be ok and the layer should reproject on the fly to the 'correct' location.