While your main computer cannot be relocated, the livebox doesn't need to be right alongside it.
I know you might think me mad but for between 5 and 10 pounds you should be able to buy a wi-fi adaptor (small USB dongle) which can be plugged into the main computer and then use your livebox in a position in the house where both the main computer and laptop can gain access.
Agree with BP that you cannot have 2 routers connected to the phone line at once - only one can 'talk' to the exchange to provide link to your ISP. Suggest you either keep the second livebox as a spare or consider selling it.
If the main computer cannot 'talk' to your livebox (while your laptop in the garden can), you might consider using HomePlug adaptors which allow you to connect via the mains cabling in the house. So one adaptor would be near the livebox, the other by the main computer. Each adaptor has an ethernet cable to link to a computer or router. Try looking at Solwise.co.uk and you should see examples of how to set up a network in a home (just from some of their diagrams re wireless and HomePlug).
There are some starter / dual packs at about 40-50 pounds here or on Amazon.
Clearly, if wi-fi at under a tenner works it is a lot cheaper, but I can vouch for "data over mains" units working well, in situations where wireless has already been tried and isn't reliable.