Is there a software solution that can verify if a disc works?

Do you get an error message, if so can you post it? Also, can you verify if these 2 disc will work on others consoles? You can also try this-

http://support.xbox.com/en-US/xbox-360/disc-drive/disc-drive-solution

Well, Darth, since we are dealing with computers (because that is what a console is: a very low-grade computer), we must assume that with all computers, when installing programs (yes, even games on a console) there will be a very small probability that the
program will not install properly.

Why does this happen? There a number of reasons. The biggest cause is because technology is not perfect and neither is software; therefore, all software is prone to problems especially during the installation process/stage.

Because of this, our solutions to dealing with malfunctioning software is to uninstall the software and then reinstall it. Since software is not perfect and will have problems, we assume that there is a greater probability that the software wlll work better
than last time if we uninstall/reinstall the software. Because of this, since consoles are similar, we arrive at the logical conclusion that if we have a game disc that is required to be installed to the HDD and it doesn't install properly, we must then uninstall
the contents of the INSTALL disc and then proceed with a reinstall of the INSTALL disc.

By doing this, we assume we will have a greater probability of the software (i.e: the INSTALL disc) working properly or better than before if we undergo this solution to the problem. This is why "install then delete the installment, then re install the update"
is considered a valid solution to most software install problems (including consoles).

Have you tried installing the games to your HDD? If you can and It still freezes it may be a software error. Does the problem only persist with Skyrim? Have you tried other disc? For disc read errors try this:

support.xbox.com/.../disc-drive-solution .

Sometimes there are software revisions that aren’t added to the white list

Please clean the edges especially, Xbox discs read outside in

But you should try it on another, preferably 360 console to verify the disc is still good

Hello,

If you've already tried the solution steps noted in the Disc Drive solution guide
here and none of your games are working, then unfortunately this means that your console has an issue with it's disc drive and it would need
to be repaired.

There wouldn't be any other way to simply troubleshoot this with you further as it's a hardware issue not a software issue or a bug that can be fixed.

I understand that your console is out of warranty, but if you'd like to play on your console you'd need to get it repaired, this can be done by clicking this link
here.