your suspicions are right
you need an adsl broadband modfem connected to the pc and then a wireless access point also connected to that "sever" pc to transmit the broadband to the laptop.
Alternatively, you would be better with an all-in one broadband modem/router/network switch/wireless aceess point.
Both your pc and laptop can then connect to this wirelessly, to access broadband and to share files and printeres etc.
Belkin/Linksys/D-Link?netgear all make them £70-£100 plus wireless card for laptop etc.