Thanks for that information. It appears that Disk Cleanup Pro does the same tasks as the excellent freeware program Onyx does. But, Onyx can also Repair Permissions, which could help.
I don't know what Secure is. Also, how did you rebuild the trash? I've never heard of that, nor have never needed to do that.
That's good you are using Carbonite. And, it sounds like you have a lot of free space.
What is needed (or would help) is the Verify and Repair your internal drive in an "external" fashion. It appears that Carbonite is not bootable. So, in your case, you will need to boot to the (hidden) Recovery HD partition, and run Disk Utility from there to Verify and Repair your internal drive, both at the Volume (ie, top) and Partition (ie, secondary) levels. To get to that Recovery HD partition, you would need to boot (or re-boot) your machine by holding down the Command and R keys. This link explains that partition:
https://support.apple.com/en-us/HT201314
Just be aware that if something goes wrong, you'll need to restore your "stuff" from the Carbonite backup.