Do you have an internal or external antenna? Does you have an signal amplifier, signal splitter or switch connected?
If the TV was previously connected to this antenna and received multiple channels, check the orientation. External antennas can turn under some conditions. With digital (ATSC) signals, this can be a significant issue, as the tuner may not see enough of the signal.
If there was an powered amplifier attached, check if the unit is getting power. Next check if the signal improves when the amplifier, switch or splitter is removed. In my house, usually only a few channels will be initially blocked by a faulty amplifier. In that case, the amplifier turned into a signal filter for a section of the VHF range. Replace the amplifier or switch if it faulty. If you are using a switch, try an amplifier/splitter that will limit the signal attenuation.
to check if where the antenna should point. Antennaweb.org assumes an external antenna and gives very conservative channel lists.
If the problem persists, check if another TV tuner works when connected to the antenna. You could connect a tuner box between the TV and the antenna as a solution. Tuners vary in signal strength sensitivity. Alternatively, replace the TV or the input board with the tuner. (If the TV is under warranty, contact the manufacturer. However, for most small TVs (under <32"), the repair costs are not worth the effort. Sites like www.shopjimmy.com can tell you if parts are available - this site specializes in parts from TVs that were damaged in shipping.)
I hope this helps.