HijackThis! is a tool that scans your computer and provides information about what's installed, as well as the ability to remove things. People who know a lot about removing malware can use it to diagnose whether or not you have malware and the best way to get rid of it. For example, you might run HijackThis! and post the results at the Bleeping Computer forum so the experts there can analyze the results. Then they might tell you to use HijackThis! to remove something which is malware or they might suggest some other tool.
HijackThis! is not an antivirus or anti-malware.
Most computer users shouldn't attempt to remove files with it without instructions because it is easy to remove things you never heard of that are actually part of Windows.
My daughter got a bad Trojan and after reformating her computer and getting rid of it with malwarebytes it keeps trying to reinstall (malwarebytes pops up and tells her it has blocked it.)
I'm not sure how she could still have the Trojan unless she used an infected backup or is visiting a website that is infected. If she saved any files before formatting, those files might be infected. There is the possibility of a firmware virus, but those are rare. As Draclvr said, it could be a boot virus. There is also the possibility of a false alarm, but I wouldn't count on it.
Virus can hide in several files on a computer and then lay dormant until they think it's "safe" for them to reinstall. You can remove 90% of the virus files, but if you miss one, it has the capability to reinfect everything. This can be time-dependent (e.g. - try to reinfect every 2 hours) or it can be dependent on the user's actions (e.g. - every time the user uses a certain program, the virus attempts to re-infect -- or every time the user visits a certain website, the virus attempts to re-infect -- or every time the computer is rebooted the virus attempts to reinfect, etc.).
I suggest she go to http://www.bleepingcomputer.com/forums/
and ask what to do. There are experts there who can best tell her how to get rid of a stubborn infection. Check their instructions page at***Am I Infected? What do I do? How do I get help? Who is helping me?***
They have so many people asking for help that they have a specific procedure they want you to follow to streamline things. Their instructions page should tell her how to submit her problem.