OK.
I do not know which window manager (KDE, Gnome, ....many more) you are using, but the principles will be the same.
1] To check the
noexec business. Use your file manager to navigate to the file
/etc/fstab, and click or double-click the
fstab file. It should open so you can read it. Does it have a line that refers to
cdrom that also contains the word
noexec? If so, that is why you cannot execute programs on the cd rom.
2] You can also navigate, using your file manager, to find the file you want to execute. Left-click & Drag that file to your desktop. Let go of the mousebutton. Choose "Copy here". Now you can probably execute it.
Having said that, you do not normally have to run files on a cd, and I wonder exactly what it is you are trying to do. If you are trying to install software, your distro's package manager is probably the easiest way to go.
It looks as though you are
really new to linux if you do not understand about permissions and the importance of "root". I'm sorry to say that you do need to do a little reading if you are going to have fun with linux.
There are many guides on the net (& google is your friend!). Here's one:
http://www.linuxnewbieguide.org/
I do not know much about mepis, but I installed kubuntu (Dapper6.06) yesterday and I am hugely impressed: It would be a very good starting distro for a newbie.
It is a 1 CD download (easy with broadband) from here:
http://www.kubuntu.org/download.php
Then see
http://www.krazypenguin.net/ and click on "Ubuntu Dapper Guide" which will help you install all the software you need, and enable useful things like mp3 playback, DVD playback, Flash, Java, NVIDIA & ATI video drivers etc.
Have fun
HTH