Many distros do not install because of low memory on some old computers. I have a laptop for which, sans swap file, Ubuntu won't even boot and yet I have installed Open SuSE on it.
Never mind what the 'systems requirements' say. Many well known distros like ubuntu, opensuse and fedora can be made to install on low memory computers if you install a swap file first.
How to do it. Plan your basic partitioning. Download and burn the GParted Live CD. This Software can also be made to boot from a usb stick.
Boot, delete or move existing partitions and install a /boot and swap partition in the low numbered cylinders. (Old hardware is often subject to BIOS Cylinder limits. The /boot partition is used to insure that your kernel image and initrd are in partitons that satisfy these limits.)
With the Swap file in place, you can almost install your Distro as you would normally.
If the Distro installation procedure asks for permission to use your swap file, say "yes".
Do not let the distro installation procedure automaticly repartition your hard drive, because it may attempt to move the swap file. It won't work to try to move a swap file that is in use.
Specify "manual disk partitioning". This has different names for different distros.
During repartitioning, you can do anything you want except move or delete the swap file. (If you need to move the swap file, you will have to abort the installation, and go back to the beginning and repartition with the GParted LiveCD.)
Once the disk repartitioning phase is complete, the rest of the installation usually procedes normally. If you are installing on the typical piece of junk, expect everything to proceed slowly, much more slowly, than you are used to.
There are also other tricks to install Linux on computers without a CD or DVD drive.