As long as you have this meter on a voltage range, and you don't short anything, you should not have anything blowing up.
And you have established that the PSU needs to be in the TV to power up correctly then you're going to have to do tests with it in place.
No need to measure across the capacitors, the measurements you've already done pretty much confirm that.
Now you need to find all of the low voltage DC rails and measure them. They may be marked where the cables from the PSU go to the other board(s).
First with power on, but TV off, then with TV on, bu in standby (if there is a distinction) and then adter you try to turn it on.
I am expecting to see a standby power supply operating with the device in standby.
What will be interesting is what changes happen when the power is turned on.