I installed 17.2 Mate on top of my existing 13 system that had an issue with recognizing my mouse I couldn't figure out.

What's the correct way to restore existing applications such as chrome? I'm assuming using the command /opt/google/chrome/google-chrome isn't correct and there's a PATH file somewhere I need to update. Thanks.

What do mean "restore" ?.
How did you "install" 17.2 - update or full "clean" install from CD/USB ?. Did you have a backup of /home (or separate partition ?).
Have you reinstalled Chrome since 17.2 ?.

You provide better data, I (we) will have less questions before we can even start.

Let me try this again:

My old system running 13 had an issue where I restarted it and could not get past the login screen. Everything was frozen so my data was intact but I could not get in.

I got 17.2 on a live usb, booted from that, and installed 17.2 in the existing root and swap partitions 13 was living in. So now my computer boots into 17.2 with all my previous data, Desktop, Music, etc. intact. Chrome for example, is also still there but I'm typing the full path to start it. Same with some other software such as Crashplan. If I reinstall Chrome, will it overwrite my existing Chrome data? Can I stick with using the Chrome that's already here?

No. System install will not write into your home directory where the user data is stored.

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Thank you, good to know Linux is smart.

This nearly always works. Sometimes when there is a large version change some options will change/disappear, so the user experience may change, but it usually "just works" as we would all hope.