Greyed out boxes even though the view and object display set to high quality and links fine

I received your files, and I was actually able to reproduce your issue.

One of my suspicions is correct; it was an incompatibility with the previews (proxies) that are attached to the EPS files by Sibelius 4 (which is what you used to create them). Based on a quick search, I found several anecdotal reports of Sibelius 4 EPS preview problems. It seems newer software doesn't like the one-bit previews Sibelius added. Hence, your new InDesign install is having an issue reading them, so it's defaulting to a grey box when it fails to read them properly.

Rest assured, your EPS files are actually fine otherwise. Ironically, they open perfectly in my Mac InDesign... It only seems to happen with the Win version. So, what to do: Since I doubt you have the ability now to reopen the files in a newer version of Sibelius and resave them as new files, I suggest the following:

You can try option 2 first, but I recommend option 1 to solve the issue going forward.

Option 1). Convert all the EPS files to PDF, and replace them in your ID files. The easy way to do this (assuming you have ANY version of Acrobat that's not Reader) is to open them in Acrobat, which will invoke Distiller and render the file as a PDF and save it as such. (You can also right-click on one of them and select Convert to PDF if it appears. OR If you happen to have an Icon of Acrobat on your desktop, you can simply drag the EPS files onto it to start this process. If you get asked whether you should trust the file, say Yes.)

Option 2), If you don't have Acrobat, let InDesign create its own previews for the existing EPS, so it ignores the bad embedded preview/proxies. First, In your ID Display preferences, check which setting you have. If you have it set to Typical (default), change the setting for Vector to High Resolution instead of Proxy. Or, change your Display Setting to High Resolution which already has that setting for Vector.

Now, open your ID file and save it as an IDML file. Then, reopen that IDML in ID and it should recreate the previews in high resolution and your links should now show (This worked for me in my tests).

Alternatively, you can Relink each file in your Links Manager (making sure you select Import Options so you can select Rasterize Postscript instead of Use Tiff Proxy).

Option 3) Open the EPS files in Adobe illustrator and resave them as new files, either AI or PDF. Based on your two sample files, this is the last ditch approach, as they open weird because of the way Sibelius cropped things, so you would have a bunch of work cleaning that all up.