Technically, yes, you could - it's called datacasting. However, it's not something that you should seriously try to set up unless you have serious practical commercial radio transmitter experience.
Some people (PDF) are working on doing exactly that using regular FM radio, and I have spoken to them about many of the issues they face -- here are some important points from that discussion:
First of all, you would have spectrum licensing issues. Unless you already own a radio/TV station and have a license, you can't just start broadcasting on the TV band. You would likely have to find some existing TV station to work with. That's doable, but you'd likely have to work pretty hard to convince them of the benefits.
Much more importantly, there would not be an easy return path back over the air, because you can't have all the computers. (The paper to which I linked above describes a protocol that is specifically one-way and requires no response from the end user.) First of all, you need some way of receiving requests for data from the user, and you also need a way for the underlying TCP ACK packets to get back. The way that Satellite Internet providers do it is that your data to them travels over the phone line, while their data to you comes through the satellite. You could do the same thing with a phone line, but it's not going to be simple.
Additionally, there is the issue of security. Broadcasting your Internet traffic out into the air for all to see is just asking for trouble. You need some kind of encryption to protect your traffic, as well as some kind of authentication to verify that what you are receiving wasn't sent by the pirate station down the block. While Cable and Satellite Internet also have these issues (because they are shared bandwidth systems), they mitigate the former by having your modem filter out traffic that isn't yours and the latter by assuming that no one else has the transmitting equipment. You cannot make either of those assumptions with terrestrial radio.
Finally, there is the issue of bandwidth. American Digital TV standards allow for broadcasting up to 19 Mbps per transmitter. If you could dedicate all of that bandwidth for a single client, that would be pretty good. However, if you have multiple clients and you have to multiplex their data on that stream, you'd see a very quick drop-off in network bandwidth. Additionally, if you were working with an active TV station, they would also need a significant portion of that bandwidth for the TV signal itself, leaving you with very little bandwidth for your data.