how to recover from a boot kernel panic

I have an older (5+ years) Mac mini. It is a Model A1176 with Core 2 Duo processor, 2x512MB RAM, 120GB hard drive as read from the back panel. It used to work fine when I occasionally booted it up but a couple of months ago it asked for a software upgrade which I did. I does not boot ever since. It says "you need to restart your computer, press the power button for a few seconds...". Basically kernal panic. I don't have the original software DVDs, keyboard and mouse. I have only windows and linux machines I can use as of now, no access to another Mac.

I have tried a few things.

1) Connected only a keyboard (I only have windows keyboards, and I have tried two of them) and a monitor. It accepts certain key combinations at boot, so it recognizes the keyboard. It can eject CD/DVDs with F12, show boot options using the Alt key and I am able to reset the NVRAM (the startup tone playing twice confirms it I guess).

2) I tried to get into recovery mode, but it is not there as this is an older model.

3) Tried a live DVD of Ubuntu 14.04 x64 (did not boot) and 11.10 32 bit i386 (boot failure).

4) Downloaded a Mavericks ISO, bought a new 16GB HP USB thumb drive and used Transmac to load it. While pressing Alt during boot, it shows the option to boot from this USB drive but when I select it, it cannot find the boot folder. It tries to boot from the USB stick but then flashes a folder icon with a question mark and then goes back to booting from the hard drive. I realize I may not have a license to run Mavericks but was hoping to find a way to fix my exiting installation using the USB drive instead of installing Mavericks.

I would like some help in recovering whatever version of OS X I had on the Mini and be able to log in to my account. I will then attempt to make rescue DVDs.