Samsung UN58J5190AFXZA (Version IS01) No standby light

The standby light means the tv is plug into the wall and getting power. A power surge can wipe out a tv and still leave the power light on.

It has a reset button on the lower back right hand corner; push that button.

Hello ? Is there any sound?

Screen coming on when the main plug is removed is normal, that happens on most TV's...Are the spots that have no volts supposed to have voltage? there is a legend on the board to tell what voltages belong no what pin, check that

Those blinks [flashes] are fault indication (Error Codes). From the number of blinks occur at one time switch ON, you can get an idea about the faulty circuit section inside it. This will make repair easy. These are called blinking codes. Make sure about the exact number of blinking of the standby/power LED, by switching On & OFF the set, for at least two times. Count it carefully. If you wish to get some details, check the site linked here. It has details about blinking codes, and fault locating procedure, to many popular brand TVs and other devices.
http://homenol.blogspot.com/
http://electronicshelponline.blogspot.com/
If blinks continue without any pause, the main board is faulty.
Search the site by type in the "brand name" to your device, [Exclude the model number] in the "Search box at the top right of the display window of the Homepage" to get gathered related posts.
Counting the number of blinks to Philips TVs is entirely different to that of other brand TVs. It is not a direct count procedure. The site have details about how to count the number of LED blinks [Fault Codes] to Philips brand TVs are given; along with details of the faulty circuit location.

Samsung told me this was a common problem and I would have to have it serviced by an authorized repair facility.
My problem ended up being the internal power supply, but they also told me the main boards burn up.

Yup I would tend to agree it's probably the PSU... It shouldn't be too expensive to fix, probably an hour or so labour and either parts OR a complete new PSU, in saying that ensure ya take it to a reputable service place.. and get a "quote" B4 allowing to continue.