Consider the current technologies that exist today that make this possible:
The first professional wireless network was developed under the brand
ALOHAnet in 1969 at the University of Hawaii and became operational in
June 1971. The first commercial wireless network was the WaveLAN
product family, developed by NCR in 1986.
1991 2G cell phone network June 1997 802.11 "Wi-Fi" protocol first
release 1999 803.11 VoIP integration
A wireless network does not seem likely, then, since commercially they were not available until 1986.
The development of the "short-link" radio technology, later named
Bluetooth, was initiated in 1989 by Nils Rydbeck, CTO at Ericsson
Mobile in Lund, Sweden and by Johan Ullman.
Bluetooth was invented after 1989, so no there.
The Arduino project started in 2003 as a program for students at the
Interaction Design Institute Ivrea in Ivrea, Italy, aiming to provide
a low-cost and easy way for novices and professionals to create
devices that interact with their environment using sensors and
actuators. Common examples of such devices intended for beginner
hobbyists include simple robots, thermostats and motion detectors.
2003 is much later than 1984, so another no.
That means it would have to be wired. The main character would need to understand how to wire every electrical component in his house and create an interface to the PC. Since this was the dawn of affordable personal computing (in the home, not just at work), the likelihood that an end user (and say, not an electrical engineer at IBM) would know how to create the necessary interfaces for each class of his electronics (TV, thermostat, basic electric circuiting) is very low to nil.