MacBook (White 2008) hangs unless in safe mode

I have an old MacBook Core 2 Duo 2.1 13" (White-08) that I'm trying to upgrade for my daughter to use for basic tasks such as going online and doing homework as it's been sat in a drawer for a few years doing nothing. It needs a new battery but is operating using the charger for now.

However, it will only boot in safe mode and hangs on the grey screen even when booting from external USB or DVD. I've tried both the 10.5 and 10.6 install disks and it appears to starting booting from them (eg. I can hear the DVD drive whirring) but it hangs at the same point and the spinner stops spinning.

In safe mode, I tried deleting the existing admin account and creating a fresh one but that didn't help.

I have also replaced both RAM modules from the original 2 x 512mb to 2 x 2gb so I know it's not the RAM causing problems. I also did some trial and error swapping modules around as well as running Apple Diagnostics and no errors where flagged.

I can boot in single user mode and perform fsck and it says the volume appears to be ok but when re-booting it hangs again and the spinner stops spinning at the same point. I've left it overnight and it doesn't progress past the grey screen.

I tried booting in verbose mode but it gets stuck on the line "airport: link down on en1". Because of that, I tried deactivating airport and ethernet whilst in safe mode and re-booting but that didn't help either.

I'm now out of options, can anyone think of anything else I can try? I was thinking I could run the MacBook in target mode and run disk utility on my MacBook Pro (retina, mid 15) but it doesn't have a firewire port to enable me to do that unless there's another way?

Any help would be much appreciated!