While my initial PurplePayday argument was that this slump was the result of ubiquity (us becoming accustomed to computers and internet use), Michael suggested there might be another reason: the bursting of the dot-com bubble.
Curious, I made a chart of the closing price for the NASDAQ for the same years as the show (in light gray) and superimposed it on the computer count on Law & Order (dark gray, with the running-average count as a red line). There is a striking parallel: a slow incline followed by a spike around 1999/2000 that shows up in both. The charts diverge toward the final seasons; while Law & Order did build storylines around the recession of the late 2000s, this didn’t effect the appearance of computers in offices and homes.
A quick Google Ngram chart for close to the same period (1990-2008) for the words computer (in blue) and internet (in red) also shows the same slump in the early 2000s.