Samsung flat-screen TV model LNR328WX/XAA has no picture. Sound is okay. I suspect the power supply board has failed, and would to confirm that, before I order a replacement board.

It sounds like the screen may have failed, that means a new TV will be needed.

Fault to the main power supply regulator section. Either it will be a separate board, or the part of main board. Check and replace damaged component/s at its main power regulator [SMPS] section circuit. Contact any service technician. If you wish to get some details; check the site linked here. Pull up older posts.
http://electronicshelponline.blogspot.com/
It will be best to replace the power supply regulator board as card basis rather than making "Surgery" to it; which usually will make loss for both money and time. Even though you can make it right, it will cost around an amount equal to the cost of a new board; including the cost of (spare parts + service charge) More to say, most of the spare parts to it will be difficult to get from open electronic spare part market. This is true to most of the flat panel TV power supply boards; irrespective of its brand and screen size.

Replacement displays are the most expensive part of the TV and getting a new one will cost more than a replacement TV. You can check on Ebay for a unit that will not power up and you may be able to get a screen cheap enough but it most cases if the screen is broken then the TV is not worth repairing. Sorry

HGi:
This model is nortorious for Y-sustain board failure, replace the Y-sustain board and you should be good to go. The Y-sustain board is the one while standing with back off the set is the board on the left side of the television.

sounds like P-LOGIC MAIN

Sounds like the power supply board has failed, VERY common problem. You can call 1-800-samsung for the nearest service center.

CHECK POWER SUPPLY BOARD ...OR REPLACED
POWER BOARD NO:
Samsung BN44-00167A BOARD, POWER (VERISONS SX07,SX05,SS03,SQ01)
Samsung BN44-00165A BOARD, POWER (VERSIONS SX08,SX06,SS04,SQ02)

I suspect that you may need to replace the ballast for the lamp and the power supply board.

Either of those, so check both.

I think you need to exchange the Main Board.