George...I hope you haven't thrown your box or packing materials away yet.
I also thought there was no power cord included...but it is there. You need to look on the end of one of the styrofoam bar supports when you open the box and pull the unit out. It IS there wrapped and fitted nicely into an end. The unit however, does NOT include the cable to connect your unit to the T.V. itself and I got a bit frustrated when I tried to connect using a standard component cable that I had (double-ended with both Red and White connectors on each end). Nothing. I ended up purchasing a Belkin Stereo Cable for $4.98 at Walmart...connecting the single end to what I believe is the output connection on the back of your T.V. and connecting the dual Red & White line connectors to the appropriate points at the back of the bar unit itself. You may or may not have to also go into your T.V.'s sound settings to choose "External" for speakers. I didn't have to do so with this type of connection, but this may be different from one HDTV to another...I'm not sure.
Also, be sure that if you are using this kind of connection (stereo cable) to your unit that you select the AUX button on the bar's remote then use the up/down arrows to increase the sound -- perhaps turning down the T.V.'s standard speakers to test and make sure you are hearing the soundbar itself.
The blue lights on the top of the bar will light up from left to right as you increase the sound. You also have some basic treble and bass adjustments on the remote as well. Plus you can pair to Bluetooth if you want and just listen to your music by itself on your bar.
Hope that helps a bit.
Yes. You should find an AC adapter inside the box.