This may be ran over a lot of times on this forum, but even though I read some of the answers I could find, I am still puzzled. I am a total noob at Linux stuff.
I have a really old IBM Thinkpad 765D with 3gb hd, 133Mhz processor, 64MB RAM and I'm trying to install Ubuntu Feisty Fawn (7.04) on it. The problem I have is that every time I select to install it in the menu, a few seconds later I get an error
"[ 000000000]ACPI: Unable to locate RSDP"
then it locks up and runs my floppy for some reason. I'm not sure about the first part, but there are only 0's and a big space before them, if that matters. I even tried to turn off acpi in the boot string, but it skips the error and locks up. It's a live desktop CD. What can I do to fix this?

I don't think this is going to work, anymore than you'd be able to install vista on this hardware!
You might get somewhere with a minimal distro like Damn Small Linux: http://damnsmalllinux.org/

I would also try.

Puppy Linux 3.01
Wolvix Hunter 1.10
MEPIS AntiX 7.0

And possibly Zenwalk 4.8

Alright, I might get Puppy Linux. One question though, will any Ubuntu-based Linux distributions run on my system?

You could try antiX Spartacus. It uses Ubuntu Dapper repos, but is Mepis 6.5 based.
You could also try BeafanatiX.