Personal data "leaking" to another computer

[robol]

Hello,
Recently I've built a shop on Presta 1.7.6.5 . Before introducing it to the general public I've asked my friends to test it. Everything works fine on more than 10 PCs. 
However, there is a strange and nasty problem on one device with Windows XP SP3 and Mozilla Firefox. When finishing the order, fields like name and e-mail are already filled with data from another client who made an order earlier and created an account! There is no way, that PCs are connected (google account etc).  Moreover, if I delete these data and put some new I get information that e-mail and password are incorrect and cannot proceed.
I've cleaned all orders with Prestashop cleaner and once again asked friends to test it. The situation happened again. On this one device with Windows XP fields name and e-mail were filled with data from another client (from other PC than in the first case)

Please help