Instead of paper clips and cardboard, consider a pachinko like marble
based computer. (claimed to be Turing complete, if you expand it enough)
https://upperstory.com/en/turingtumble
It's bulkier than a mobile phone.
or relays? :
https://www.amazon.com/Giant-brains-Machines-that-think/dp/B0006AS6Q4
Giant Brains : or Machines That Think
by Edmund C. Berkeley
His Simon computer was a relay based (a bit limited for modern uses), but
was an early (1950) electro-mechanical personal computer.