So I’m having trouble with these lego piece models that I’m trying to edit and reshape. It seems like a lot of the faces are disconnected from each other, not making it a solid mesh which has made it extremely hard to do anything with. Here’s a couple images, one of the normal mesh, and one where I just smoothed the vertices so you can get a good idea on what faces are connected to one another and what ones aren’t. Does anyone know a simple way of combining all of these into a solid mesh? Or at least get me to a good point to where I can have a solid mesh I can fix any small issues that come from doing it.
Hi, and welcome to the BA community,
Try this select all the vertices in xray mode go to; edit mode>mesh>clean-up>merge by distance.
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There seems to be a problem while importing files. 
Check it out in Edit mode.
If the edges are really gone, you need to connect them yourself. (Some can be cleaned up with the cleanup function)
I hope the left one is the already imported file before smoothing. If yes, then do a merge by dst as @digitvisions stated. Distance 0 should be enough if the vertices lie really on top of each other.
Also do a “tris to quads” afterwards so that you get the quad mesh restored better.
Mark the sharp angled edges as that and then add a subdiv modifier.
Good luck.