Without networking capability...you cannot connect to the Internet.
A network is nothing more than a connection between different computers. You must connect with other computers used by websites and your ISP...via your ISP...in order to have Internet access.
As for your perceived problems due to network capability...I would suspect that you have such because you are missing a large number of Windows updates which help provide security for the system. SP2 has been superseded by SP3 (which reflects over 100 critical security updates) and that, in turn, has been supplemented by well over 100 additional critical security updates for Windows XP. Running a system without these critcal updates...invites malware and is just absolutely poor security from those see fit to be a nuisance to users of the Internet.
If you are currently running Windows XP with SP3 installed, then you still need all critical security updates which have been issued since SP3 was first released.
As for system security...the answer to good security is good security practices by users, not trying to do the impossible
Just as a general read...you might look over Answers to common security questions, Qman - http://www.bleepingcomputer.com/forums/topic407147.html
We also have various forums that deal with malware, system security, etc. You may want to visit one of those for ideas on how to avoid what you describe as past problems.
How to Protect Your Computer from Spyware and Adware - http://www.microsoft.com/windowsxp/using/security/expert/honeycutt_spyware.mspx
Basically...no one can gain remote access or any other type of access to your system...if the correct practices and settings are incorporated in the care of the system.AV, Firewall and Privacy Products and Protection Methods