MacOS – Format Macbook 2, 1 running 10.4.1

You should be able to use dd to destroy the partition's header. You can then format (erase) it and run the install.

From the installer run Terminal and type the following:

dd if=/dev/zero of=/dev/disk0s2 bs=1024 count=1024

Do be warned, this will irrecoverably destroy all data on that partition. But it looks like that's what you're expecting. Make sure you don't accidentally target the wrong thing.

Also note that I haven't done this, exactly. I've used this technique to destroy the entire partition table, not just a single partition. But I think it should work.

When you're done quit Terminal and run Disk Utility. You won't get any complaints about Core Storage.

The graphical "noise" makes me think that either the graphics drivers have been corrupted (and by the sounds of it, likely more OS components), or there's a hardware defect.

• Does the "noise" appear when the Apple logo is on screen, or just afterwards? If during the Apple logo, it's more likely a hardware problem, since that boot screen isn't based on the OS install. If afterwards, it may just be a problem with your install.
• You can try booting off the Recovery Partition by holding down command-R when you boot.
  • If this goes well, then it's likely a problem with your boot partition being corrupted. The recovery partition includes Disk Utility, which will let you run a basic check of your boot partition, which may or may not be able to fix things.
  • If this fails, then you either have a hard drive issue, or some other hardware problem, in which case you're almost certainly going to need to consult an Apple Store or Service Provider.
• You can also attempt to boot off an external drive as segiddins suggested in the comments.

Sorry I can't be definitive, but it's hard to say for sure without having the machine in front of me. Try some of these and let us know how it goes, and we can help narrow some things down for you.