I think this is an important finding because it helps shed some light on the socioeconomic disparities in educational outcomes. We know that kids from higher-income households do much better in school than poor kids. But that of course raises the question of why that is exactly or what one might do about it. For example, would cash transfers to low-income parents make their kids do better in school? If access to home computers was associated with improved school performance, that would be strong evidence that simply fighting poverty with money could be highly effective education policy. The null finding tends to suggest otherwise, that the ways in which high-income families help their kids in school don't relate to durable goods purchases and may be things like social capital or direct parental involvement in the instructional process that—unlike computers—can't be purchased on the open market.
An obvious conclusion would be that kids from higher income households attend higher quality schools. A cash voucher to be used at a better school is going to have more impact than a cash voucher for a free computer. Computers aren't magic, you don't just turn them on and absorb knowledge.
Here's another study examining the correlation between computer use and academic achievement on standardized testing.
http://www.medicalnewstoday.com/releases/19387.php
Analyzing test performance and computer uses of 986 fourth grade students from 55 classrooms in nine Massachusetts school districts, the study found that the more regularly students use computers to write papers for school, the better they performed on the Massachusetts Comprehensive Assessment Systems (MCAS) English/Language Arts exam. This positive effect occurred despite the fact that students were not allowed to use computers for the test.
Conversely, the study found that students' recreational use of computers to play games, explore the Internet for fun, or chat with friends at home had a negative effect on students' MCAS reading scores. Similarly, students' use of computers to create PowerPoint presentations was also negatively associated with MCAS writing scores.
This study was part of a larger report: Use, Support, and Effect of Instructional Technology Study
http://www.bc.edu/research/intasc/researchprojects/USEIT/useit.shtml