You could try to boot a live system from USB stick. This is even possible on older machines, but with some detours.
You need another PC for that to create that bootsick. I recommend using the software UNetBootin to create a bootable stick. It's nearly self-explanatory.
If this old machine allows USB Legacy Emulation (found somewhere in the BIOS setup), enable it and try to boot from USB stick. If not, use Plop Boot Manager or something similar to boot from USB.
If you're able to bring up the live boot menu (UNetBootin menu, if created with UnetBootin), select Try Ubuntu. After the GUI finished loading, open a terminal (Ctrl+Alt+T) and enter the following commands:
# List partitions to find the correct one
sudo fdisk -l
# Memorize the name of the partiton with "Linux" type and "boot" flag
# Create mount directory (replace the hdd by anything you want)
sudo mkdir /media/hdd
# Mount partition into this directory (replace XY by memorized partition file name)
sudo mount /dev/sdXY /media/hdd
# Open root shell of the installed system
sudo chroot /media/sdXY
# Change password of user and drop back to live system shell
passwd username
exit
Now shut down your machine, remove the bootstick and boot into the installed system. The password should be the one entered on passwd username
.