Hi there usuariou.
I'm also using a very old PC for Kali but it's working quite well. Sometimes when I'm running a live-usb Kali session my computer also freezes. Sometime it's my wireless keyboard-mouse. I unplugged them and that's all. It's working again. But, some other times my PC freezes completely and this has nothing to do with USB wireless keyboards/mouses. This behavior is present in both x86 and x64 Kali ISO.
Try to unplug any unnecessary devices and then start Kali.
Security always begins with personal responsibility. - quietman7