It aired on BBC in the UK in 1991. Whilst not totally similar to the plot you mention the IMDb plot summary seems to have enough matching elements that this is worth mentioning.
Marcie, Reet and Thomas are three children who are stunned when for some unknown reason each kid at their school is given a really powerful computer and that the class swot is turned into a mutant by the computers and it's controller Mr. Eldritch. Investigating the three discover that the computers are a part of a plan to rule the world but they need to find Professor Polzinski. With the aid of the Professor, Eldritch is stopped. Later on, a team made up of blonde women dig up the school field to find a wartime computer Behemoth with the power to destroy the world. Super-intelligent Marcie and Eldritch battle against each other for control of the world and in another round in the age-old war of good vs evil...
The Wikipedia plot summary also mentions a lot of similar elements and gives a better breakdown of what happens in each breakdown of the episodes.
The first three episodes begin with third year secondary school girl Marcie and her two fifth year friends Tom and Reet becoming suspicious of the sinister Mr Eldritch, whose computer company arrives at the school and distributes free computers to all the pupils.
With the reluctant help of their teacher Miss Maitland they apparently defeat the threat of Eldritch, who disappears. However, the second three episodes tell of the actions of Miss Pendragon, who works for Eldritch and is attempting to revive the massive, secret Behemoth computer from its long-hidden location beneath the school.
At the end of the BBC novelisation, there are indications that Davies had ideas or interest in a potential third adventure using the same characters. A single paragraph describing the opening of an amusement arcade concludes with "...but that's another story."