I receive a message on boot (Linux Feisty for old machines) that passes too quickly for me to get the exact wording but it says something like failed to allocate memory resource.

The PC is a Pentium II, 450 MHZ, with 128 K.

Is there any way to fix this?

As root, check the contents of /var/log/dmesg. This file contains all the messages that scrolled past on startup.

After reviewing that, you'll be able to post an informative question which can be answered.

Found it, got there, and printed it out onto the screen.

The message said, "27.414903 PCI: failed to allocate mem resource to #6: 10000@fd000000 for 0000:0 1:00.0"

Next line said, "27.414792 PCI: Bridge 0000:00:01.0"

Question: What is #6?
Is this preventing me from using the PC's piddly 128K memory?
Is it important and/or possible to fix?

This PC is a Pentium II, 450mhz, 128K operating slow as death using this Linux install.
I believe I installed Ubuntu 7.04 alternate i386 onto it.

Thank you in advance for any assistance.

I don't know what that is. Looks to me like something on the PCI bus is asking for a 64K buffer and is being denied.

Run the command lspci to sort out what that is. You can get a lot more verbose output with the command lspci -xxx.