If you've replaced the bulging caps and it still clicks, then your 5 Volt standby circuit on that power supply board should be fixed. That supply in turn powers up the TV's micro, which then powers up the relay on the power supply board.
So the power supply makes the main board's micro turn on the relay on the power supply.....
If you replaced the caps, and it still clicks, most likely the TV's micro is delivering a Hi / Low to the Pow On line. That's what actually turns on the relay.
What I like to do to see which one is bad....I jumper the Pow On line to the 5 Volt standby connection and see if the relay STOPS clicking. It'll click ON....and it should STAY ON.
To FIND the P-ON or POW-ON, look at your power supply board, see if it has this little box of information right by the double-row plug. The KEY is to identify the P-ON and the 5V stby, disconnect the cable from the main board, and stick that jumper on the P-ON and 5Vstby holes and make the relay turn on.
Check this --
You see that? I wrote that up for another customer, because he sent me a picture of his plug. I showed him that one side is odd, the other side is even numbered wires....the white rectangular box right by it has the Pow on and 5vstby marked in it.....all the info is there to see if the Power supply relay turns on, and stays on. And if it does.....then you deal with the TV's main board.
As for the EEPROM....forget it. Samsung doesn't just sell the EEPROM as a part.
To get the main board -- there is a BARCODED sticker on it. It has a BNxx-xxxxx number.
Get that number and you're halfway there.
And yes, I am assuming you have certain technical skills since you think the EEPROM is IC 2103.
We can't fix it that way. I didn't make the rules, Samsung did. I can only point you in the right direction, and get you up to speed on how Samsung Techs fix problems like yours.
I'm here if you need me. Of course keep in mind it's Sunday, I have chores to do, and yes, I am across the big pond. I check in once an hour for responses from mulitple customers, but I am HERE.