Your HDTV should have a digital TV Tuner (ATSC) which may need an indoor antenna. Change your TV's input selector to TV or Antenna or Digital (probably one of those three) and scan for channels. If you don't get any channels, then you do need an antenna. Probably another $10.
A lot depends on where you live, but you should be able to connect directly to an antenna, as Wolf was saying.
Go to: http/www.antennaweb.org/aw/welcome.aspx
Click on "Choose an Antenna" and fill in the form. (Hints: 1. UNcheck the boxes to receive mailings. 2. You don't need to fill in your address, but if you don't you'll be helped better if you twiddle with the map.)
This will give you a list of stations near you and what type of antenna you need to receive them. Generally, if you're within 10 mi of the transmitter and unobstructed, you can use an indoor antenna.
Hint: DTV requires a stronger signal than analog did. The antenna that worked for you for analog MIGHT work fine now, but might not if it was marginal on analog.
Note: DTV transmits on the same frequencies as analog did (except channels 2-5 were dropped, and some stations in your area may have moved to a UHF channel--note also that the actual broadcast channel may not be the same as the "virtual" channel that the station appears to be; for instance, you might have a "Channel 2" in your area, and it might be on actual channel, say, 34.
Which reminds me: The fact that you've had trouble receiving DTV may be merely that you have not scanned for channels. With DTV, this is a must, because otherwise, the receiver doesn't know what you want to watch or what each station "calls itself".
1. Does the Webpage I referred to tell you there are active channels in your area?
2. Do you have a digital TV (or converter box)?
3. Do you have the TV (or converter box) set to over-the-air? (After failing to get many stations on cable at RV parks, I discovered my set can be set to "cable" and then I get them all. It's possible to make the mistake in the opposite direction.)
4. Have you scanned for channels? (An absolute must, and a totally new concept for those of us who grew up with analog TV. Also a must whenever one station reconfigures.)
5. Your antenna: Plain old rabbit ears are not likely to work well, unless your local stations are actually still on a VHF actual channel (aka "RF", radio frequency--read what I said earlier about virtual channels and RF channels). There are good-yet-inexpensive antennas which are optimized for UHF (channels 14 and up) and for digital. (These usually have a ring of some kind, with or without rabbit ears.) (I've also seen ads for antennas which actually hide behind your set--don't know how good these are, haven't tried any of them.)