If needing a i486 kernel and debian testing for your HP.
There are a few choices below. The 496mb iso is the full iso with a AntiX Control Center and Icewm and Fluxbox Desktops and Synaptic Package Manger Gparted, a bunch more stuff.
The 270mb Iso is without a AntiX control Center and just comes with fluxbox Desktop and apt-get. Kinda a build your own. Smxi and sfgxi come with both downloads as well as lshw and other good command tools.
My old Laptop is close in specs to your HP Desktop
Linux Version 2.6.34-stevo
Compiled #1 SMP PREEMPT Fri Jun 11 18:50:40 PDT 2010
One 1GHz Intel Pentium III Processor, 256M RAM
1992.65 Bogomips Total
# fdisk -l
Disk /dev/hda: 20.0 GB, 20003880960 bytes
255 heads, 63 sectors/track, 2432 cylinders
# cat /etc/issue
Debian GNU/Linux wheezy/sid \n \l
Host biker Kernel 2.6.34-stevo i686 (32 bit) Distro antiX-M8.5 Marek Edelman 11 April 2010