Well I don't get very far in the installation process because while it's scanning USB ports, drives and such at the start of the installation, I get an error saying "I can't access a Mandrake Linux Installation disc in your CD-ROM Drive." I checked and my cd-rom drive is compatible with Mandrake and the md5s for the ISO were correct also.

I'm really new to this, so is there something I'm doing wrong here?

Need a little more information:
1) What kind of CD-ROM?
2) How does it attach to the comptuer? (IDE, EIDE, USB)
3) Is it a CDROM, CDRW, DVDROM, DVDRW, etc...?
4) Did you download the ISO's or did you buy the distro?
5) How did you get the ISO on the disk? What program? Did you simply transfer the *.iso file, or did you 'Burn as ISO' in Nero?

Perhaps you have a bad CD? Or your drive is sort of worn out? Did it go like it was trying very hard to read the disc but couldn't or just it just ignored the disc and told you there is no disc?

1) It's a Samsung CD-ROM SC - 140
2) Er, not sure, but I know it's not USB
3) It is a CDROM
4) I downloaded the ISOs from a mirror on the mandrake site
5) I burned them as an image

And I don't think it's the drive. I've never had any other problems with CDs, and it was still able to boot from the CD so it was readable to an extent, I guess.

personally: im bettin you burnt a coaster...
try reburning the image

Look at your CD very closely, see if there is any dirt on it. (anything that may block the laser beam) Sometimes they are really difficult to notice. You can try burning another one. CD-Rs are cheap anyway.

I tried that and it did the same thing. Could it be the type of CD-Rs I'm using that's causing this?

I dont think so. There are actually only one type of CD-R. Try using a different CD drive. Perhaps Linux loaded a wrong driver for your CD-Rom. Some Linux distros mess up on some drives. My LiteOn Combo drive literally DIES (cut off power and disconnected from the system) under Fedora Core 2 and thats one reason I am using Mandrake.

The only other CD drive I have is my CD burner. Is it even possible to boot from that?

A CD burner will work just fine. Dont worry. For your information: A CD Burner is a just CD-Rom (Reading head) PLUS a Writing head.

Ok, I booted it from my Cd burning and everything was working until the exact problem occurred again.

Anything else I could try?

So now we ruled out the CD drives and the CDs...

Something could have gone wrong in the burning process... can you discribe? It could be the software settings or the burner not working properly.

More than one of Mandrake's install CDs are bootable just incase, for some reason, disc 1 doesn't boot. I can't remember which CDs it is (I'm a SuSE user now), but it should be on the Mandrake site somewhere. Or just try the others and see if they will work.

I had similar problems with Mandrake: my DVD drive just chewed the disc (the repeating click-clunk bit). If your drive(s) are doing this before the installer errors then it may still actually be the drive. I just used my CD-RW and it worked fine.

Are the two drives on the same IDE cable? This is just long-shotting but if nothing else works then put one drive on the other IDE cable. Which one depends on whats on the other cable. If it's unused then put the master on it, (the slave on the original cable will disappear in the BIOS as it's now the lone slave drive on the cable), otherwise move the slave. This will save fiddling with master/slave jumpers. (Which is a pain). Don't bother with this unless you get desperate, because this is annoying to do and unlikely to reslove the problem.

I think it could be the cd-burner or the cd-burning process also. I tried burning the image with Nero but everytime I did that it gave me an error saying that the wasn't enough room on the CD-R. So I tried some other programs and this "Burn4Free" one seemed to work. Could that be it?

CD2 is also bootable. You should note that sometimes install hangs due to peripherals connected. It is advisable to disconnect printer and/or USB devices - it is often a USB issue. A friend of mine made his system work by transferring something as basic as mouse and keyboard from USB to PS/2.