I took a quick look at your logs where Satchfan was helping you clean things up and also your daughter's computer specification....
May I ask please if this computer is used only whilst totally isolated from other machines. that is to say with no use at all of Internet, (email etc) and removable media for example USB memory sticks, DVD's etc?
If so, despite the Windows XP operating system being unsupported by Microsoft, with great care its possible to continue using it, without the risk of immediate infection.
However it is not safe to use on the Internet anymore, (without taking extraordinary precautions) or to use it for email etc, ..........and USB memory keys and the like should now never be used without taking extra ordinary precautions.....
Some folks take the view that if they have an active anti virus and firewall to protect them then that's all they need......... nothing could be much further from the truth!
Vulnerabilities in old software and unsupported Operating Systems like for example Win XP, make this computer a "sitting target" for the bad people, the difficulties you have experienced in updating Internet Explorer from v 6 to V8 have actually done your daughter a favour, by allowing the vulnerabilities to be highlighted so she can take the opportunity now of immediately isolating the machine from sources of infection (isolate it from the internet, other computers, memory sticks and the like.... ) whilst the computer is still clean.
If she wants to continue using the computer on the Internet for example, she would be well advised to install a modern and robust supported operating system like (if possible) Windows 7 or Linux ( Win 7 has to be paid for (unless you have a copy already pre purchased) but is very inexpensive to buy..whilst Linux comes at the low cost of Free! ( but its different from Windows so may take a short while to become familiar with it)
If she decided to stick with Windows and consider installing Windows 7 then it would be wise to run the Microsoft compatibility tool to see if her machine is up to it.
She can (hopefully) download it from here:
Finally Internet Explorer 8 whilst being more secure than Internet Explorer 6 is still highly vulnerable, unsupported and its continued use leaves an open "gateway" into your daughter's computer for malicious code, viruses, worms Trojan Horses and other horrors!
Post back if you or she, needs any clarification.