I'm curious about those people who are posting that they were not "allowed" to be bored, or that they weren't always entertained in the old days. I wonder how much you were really alone and expected to entertain yourself.
I had what I think of as a pretty typical childhood for someone of my generation (I'm in my 40's). I went to school, and did some activities such as girl scouts and singing in the church choir, but I also had a lot of downtime. I certainly wasn't entertined by an adult for all or even most of that time, but I also was rarely alone. Instead I played outside, where there were always other kids; I babysat or did mother's helper type work in the neighborhood; I played with my siblings; I did things with/for my mother where we were doing things together -- helping her cook something or cut something out for her job as a nursery school teacher, or working along side her in the garden, folding laundry together etc . . . ; I practiced the piano with my mom in the background telling me occaisionally to try it again or that it sounded good; I walked up to the neighborhood pool where I swam on the swim team.
Now I'm the parent of an 11 year old boy. Since I'm a single mom, and I'm in online grad school, we're often in the situation that the OP described, where he's alone in the house with one adult who is occupied on the computer. Unless he has a friend over, he's alone in a way that I almost never was. When I look at the things that I did, most of them aren't options. He could play outside (and does go outside to walk the dog or play with the dog) but there are almost never kids his age there; 11 year old babysitters don't seem to be in demand; he doesn't have siblings to play with; the neighborhood pool doesn't allow kids under 12 unsupervised . . . So, he's truly alone in a way that I rarely was at that age, and for an extroverted kid that's hard.
OP, we haven't found a solution that's perfect. My son has a friend over when he can. Otherwise, he walks/plays with the dog a fair amount, helps around the house some, reads some, and plays computer games most of the time. He also does more camps, and outside of school activities than I did at that age, and we do a fair number of things as a family, such as going to the pool or movie etc . . .