I own a DYNEX DXLCD37-09. I am having trouble turning it on. The red "STAND BY" indicator is on and when I press the power button the green "POWER ON" indicator flashes a few times and then instantaneously turns off. My question being, is the problem the power supply board or the inverter board?

It can be related to a power supply fault , problem in the SMPS unit. Also a poor connection due to dry soldering of the drivers cannot be ruled out and so if you tap the TV while it is powering and if the power comes up it can be a poor connection. Please use a good observation lamp and armed with a good soldering iron to touch up taking acare of the charged capacitors.
please check this link for tips to repair the SMPS:

http://www.fixya.com/support/r5826301-working_switch_mode_power_supplies

Hi,

It is clear that the problem lies on your Power supply board. Please go check and get it fixed then.

Regards

Hello,

The issue you describe is consistent with a power supply board issue. This is the board where the AC goes to. This problem may have occurred as a result of irregular power supply, or excess power supply or power surge.

The TV is receiving current but cannot circulate or transfer the current to other necessary part of the TV because of the defective power supply board. You might be lucky it's just a blow fuse. Also a defective transformer can cause your TV not to power on.

All these can be checked on the power supply board.

But more often bad capacitors causes problem on the power supply board. I do not think the power board needs replacement, rather those defective capacitors is causing this issue. Open unit up and take a look at the power supply board.You will probably see one or more electrolytic filter capacitors that are bulged up in the top-not perfectly flat like the others.

The value of these capacitors will be different, most likely they will be somewhere around-820 to 2200uF/25 V( or /10V sometimes)

You can replace them with same values but I would recommend the voltage rating to be higher(like 35V for an original 25V) for reliability purposes.

What happens is,these bulged top capacitors will cause a low and unfiltered DC voltage=main board will malfunction(the relay will keep clicking until the caps are holding enough charge to bring the voltage up over a threshold point).

You can buy these capacitors at any Fry's or Radioshack store or you can order them online at vendors like "mcmelectronics.com"(look for electrolytic capacitors). After replacing these capacitor(capacitors) most likely the normal operation will be restored. Or you can by a refurbished complete power board to save you some stress from www.shopjimmy.com

Note: There may be also some other causes for this symptom ,like a defective T con board ,or main board,but the bulged top capacitors are the most common cause for this issue.

If you don't know about TV repairers, take the TV to the nearest repairman to fix the fault for you. Also, note that TV stores a lot of current, so wait a while before opening the TV back cover.

I hope this helps.

Regards.