I don't know much about phptriad either, however..
This should quick-and-dirty-ly

cover any linux commands you need.
Copying your website files:
Depending on the distro of the old machine, they're probably in /var/www/
Although, if it's SME it's /home/e-smith/files/ibays/<ibayname>/
You should check...
Using PuTTy on either machine would get you to a command prompt
Use the ssh command to work on the other command:
ssh <user>@<host>
(<host> can be a dns name, or an IP address)
Use scp to transfer files:
scp (-r) <localpath/localfilename> <user>@<remotehost>:<newpath/newfilename>
scp (-r) <user>@<remotehost>:<remotepath/remotefilename> <newpath/newfilename>
(-r means directory and it's content, <remotehost> can be a dns name, or an IP address)
Use chown to allow anyone to the webfiles:
chown (-R) <user>:<user> <files>
Use user www for files in ibays
So this would mean, from the new machine:
ssh root@youroldmachine
scp -r /var/www/html/* root@yournewmachine:/home/e-smith/files/ibays/Primary/html/
scp -r /var/www/cgi-bin/* root@yournewmachine:/home/e-smith/files/ibays/Primary/cgi-bin/
mysqldump yourdatabase > /mydatabase.sql
scp /mydatabase.sql root@yournewmachine:/mydatabase.sql
exit
mysql < /mydatabase.sql
chown -R www:www /home/e-smith/files/ibays/Primary/*
Note: If your using a specific ibay, replace Primary with your ibay name in the paths