Of the nine teams with an available car to run on the opening day at Jerez on Tuesday, Button was the only driver not to turn a wheel in anger.
McLaren described the situation as "a challenging start", and that like other teams they had "faced difficulties" readying the MP4-29 for the first of the three winter tests.
McLaren blamed "electrical issues" for the lack of running which required the dismantling, inspection and reinstallation of several major components.
Given the complexities of the new powertrain units (turbocharged 1.6-litre V6s have replaced the 2.4-litre V8s) and the new-for-2014 ERS (energy recovery system), all the teams have faced headaches in the build process, hampered by the lack of time.
But on a chilly, damp second day on Wednesday, the McLaren completed an installation lap early on, followed by a further two tours of the southern Spanish track just under 90 minutes into the session.
That will undoubtedly have come as a relief to all within McLaren, who appear to be operating without a team principal following the unconfirmed exit of Martin Whitmarsh recently.
After one of the worst seasons in the team's history last year - they failed to score a podium for the first time since 1980 - Ron Dennis staged an internal coup which resulted in Whitmarsh being deposed as the McLaren Group's CEO.
It is believed Eric Boullier, who resigned from his post as team boss at Lotus on Friday, will be appointed as Whitmarsh's replacement early next month.
On track, after two hours, Button was one of six drivers to have taken to the circuit.
The Briton was joined by Williams' Valtteri Bottas, the Ferrari of Kimi Raikkonen, Force India's Sergio Perez, the Sauber of Esteban Gutierrez and Red Bull's reigning champion Sebastian Vettel.
Vettel, who only completed three laps on Tuesday due to technical issues with the RB10 and with the first of those not until 15 minutes from the end of play, had at least matched that figure by 11am local time.
Mercedes, meanwhile, were hoping to return to the track later in the day, with Nico Rosberg at the wheel, after making repairs to the W05 that Lewis Hamiton crashed on Tuesday due to the failure of the front wing.
As for Marussia, with their car due to arrive on Wednesday afternoon after its own technical issues at their factory in Banbury, they were appearing more likely to make their season debut on Thursday.