Sounds like the boot priority order (the order the computer checks for things to boot off) is messed up.
Each different BIOS has a different layout, so the exact keypresses needed to reset the boot order is not standard. Some computers, along with the option to edit the BIOS config, also provide an option to quickly change the boot order, which is achieved by pressing a different key. Again, this varies, but it usually tells you when the manufacturer's screen comes up, the same as it does to enter BIOS config. If your computer has this feature, you can use that to change the first boot device to the DVD drive.
If it doesn't, then I'm afraid you are gonna have to figure out the BIOS config itself. As you probably already know, the BIOS config uses the keyboard for navigation, not the mouse. This can be very confusing, but most BIOS configs have several sections with different types of options. The option you'll be looking for should be called something like "Boot" or "Boot Options" or "Boot Priority" or "Boot Order" or somthing like that (yeah I know, very non-standard). Unfortunately, different BIOSes have different sections, so there may be a "Boot" section, or you may have to look through each section to try and find the right bit to reconfigure the boot order.
In general, BIOS configs let you navigate using the arrow keys, and sometimes the PgUp and PgDn keys. Some BIOSes have the sections listed horizontally along the top. The way you normally navigate through these is left/right to change sections, and up/down to select the option to change (and enter to change it). Some have the options listed vertically along the side. These often use up/down to select the section, and enter or something to change the options in that section (using up/down to select the option). However, you may have to navigate differently to this. Luckily, it will often tell you somewhere what to press to do what (although not always - again, depends on the BIOS).
If you find the boot order, you will probably be shown a list of different bootable things, and have to use +/- to move them up or down. Like everything else, it may be different (like Pg Up/Pg Dn, or something completely random), but luckily, again, most good BIOSes give you on-screen instructions somewhere. If you move the DVD drive to the top of the list, that should be the first boot device, and you should be able to boot from it.
Of course, with some BIOSes you don't move the device up and down, you actuallyl assign a value to them. If this is the case, set the DVD drive to PRIMARY or 1 or whatever option it gives you that means "first". You probably do this by selecting the device using the arrow keys, and pressing ENTER and using the arrow keys to select (maybe number keys, although I have never seen this).
You are right, it is confusing
Unfortunately, since the boot priority is messed up, there isn't really any escaping from the BIOS
EDIT: Of course, if it's just the data you need, you can always take the hard-drive out and put it in a 2.5" external USB enclosure (lets you browse your files from another computer)
EDIT 2: Unless what you mean is you can boot off CD drive, but it errors when you boot off the CD drive, and you have a DVD drive but can't change that to primary boot?
