Testing power supply and led strips on LED tv with seemingly working t-con board and main board. TV is an LG 50LN5400. The TV has sound and apparent picture using flashlight test.

Based on the symptoms you described, it sounds like the problem is likely with the LED backlight strips on your Samsung TV model DF400BGLV1H. When you disconnect the LED connector, the standby voltage comes back, and the T-CON board blue LED lights go on and the boot sound. Also, the fact that the power supply board measures 225 volts on pin 1 and 2 of the D+ on the connector when disconnected and toggles off when connected to the LED, suggest a short on the LED side.
It is possible that one or more of the LED backlight strips may have failed, causing a short and preventing the TV from powering on properly. In this case, replacing the LED backlight strips would be the most likely solution to the problem.
Keep in mind that it is always a good idea to double-check all connections and components for proper function and continuity, before replacing any parts.
It's recommended to seek the help of a professional technician or contact Samsung customer service for further assistance, especially if you are not familiar with TVs. Also, make sure you get the right replacement parts and follow the instructions.

Likely the diodes are also blown, and are what caused the capacitors to blow.

1. Disconnect the cable between the main power supply & main board, supply AC to the TV, if the LED strips are OK, it should light UP, if not replaced all of the LED strips.
2. If the back lights light up, but no display or sound, replaced the main board.(after you re-connect cable).

The problem is defective LED back lights strips inside of the panel.

Check and replace damaged component/s at its back-light inverter board, or replace this board as card basis. If you wish to get some details; check the site linked here. Surf the site with patience. Pull up older posts. It will be best to replace the inverter board as card basis.
http://electro-medical.blogspot.com/
http://electronicshelponline.blogspot.com/
To some model sets; especially LED back-lighted types; the back-light inverter circuit will be part of the main power supply board [SMPS]. In such cases, the power supply board might need replacement. To some models sets, the back-light inverter and SMPS section circuit will be integrated at its main board itself. If so; the main board should be replaced. To some models of sets, all these section circuit will be integrated at its main board. If this is the case, you have to replace the main board.

Before backlight, I would always suspect TCON board

Chance your led strip if you are sure that your power supply led module is working perfectly

usually bad power supply, Where did you source your part? return/exchange it. Bad LEDs/ possible but not as likely, Tcon working if you can see images with flashlight. You must also have backlight on signal from main board ,check for 3 to 5v on labeled connecter on power supply. UPDATE---47" & 50" LN series. This model has had LED problems if your TV acts as described by Mr. Hughes in is answer to this problem you have bad LEDs

Definitely odd for sound to come through and not sound, especially via an HDMI connection.

I would contact LG for support, your TV could be defective.

Good luck