I have just bought a Doro 8075 additional handset... (by 3 users)

If it came with it's own cradle and charger then it should work. Perhaps it's a faulty one.
Make sure it's fully charged before you try programming [about 16hrs] then try again.
If it still won't log on to the base unit take it back to the shop, take your user manual, make sure you don't leave it there.
You can then with the aid of the book go through the progamming sequence with the sales rep so he/she can see your doing it correctly. If you are doing everything you should, and have done at home ask them to change the unit, it may be faulty.