As you have not posted a complete detection entry, we cannot see what software was detected as the trojan.
It looks like you may have picked up a PUP, a Possibly Unwanted Program. While they are annoying, they do not cause damage to your system. Some people actually want the 'Features' offered by these programs. They are usually downloaded alongside a legitimate download when you do not uncheck the option for the additional download.
Norton products concentrate on malware that can damage your system, that is why some PUPs are not detected. Other security software may detect these PUP's more aggressively as trojans.
I wonder what Norton Full Scan would have reported before your Adaware Antivirus Scan.
I wonder what Malwarebytes Scan would have reported before your Adaware Antivirus Scan.
From this distance IDK what Adaware Antivius found.
Adaware detected and then I proceed with the automatically cleasing. Which took around 10 minutes to clean.
I am very desappointed with results of Norton! I had this bad experience before as McAfee detected a Tojan on my machine running it from the OS on security mode. I simple do not like McAfee software design. But it detected a trojan while Norton did not. Which worried me at that time.
I complained with Norton help desk, but they never answered back.