After ensuring the computer is malware free, you can also try this ESET tool which restores commonly infected disabled services.
http://kb.eset.com/library/ESET/KB%20Team%20Only/Malware/ServicesRepair.exe but these are the services required for Internet connectivity set to either Auto or Manual.
For any that can't be started, right click on them, select Properties and check their Dependencies.
Some of the Dependencies can be found in Device Manager/View/Show hidden devices/Non-Plug and Play Drivers.
You should also check that Windows Firewall is also started.
COM+ Event System
Computer Browser
DHCP Client
DNS Client
Network Connections
Network Location Awareness
Remote Procedure Call (RPC)
Server
TCP/IP Netbios helper
Wired Autoconfig is set to manual.
Wireless Zero Configuration (XP wireless configurations only)
Workstation