LC-52D64U (Sharp Aquos) component ID

[Plane Nuts]

I picked up a Sony LC-52D64U (Sharp Aquos 52 in) TV that will not turn on, while testing Main P/S board DPS-304BP-1 I accidently shorted out a resistor and unfortunately it does not have the lines on it so I don't know its resistance. it is R7641 in the attached drawing and have attached pictures of what is left in case someone familiar with these resistors can identify it or has one of these boards and can check what is it. would like to know resistance and what type it is if it is special, and will a regular resistor work.

After looking at the pictures on the computer and not my phone looks like 0.1 ohms does everyone agree?

[R_J]

Looks like 0.1Ω, .5 watt fusible flame proof, If the resistor is open, I suspect Q7601, Q7602 are also shorted

[Plane Nuts]

Thank-you R_J,

I Replaced the part, and luckily it did not blow anything else. I tracked the main issue with the TV not turning on to a shorted mofset P/N K3706, I put in a P/N 13N50CF, and at that point the TV would try to turn on but would shut down after about 5 seconds. After a few tries it shorted out again. I am wondering if it is because the MOSFET specs was too far off what is supposed to be there or there is something else loading it to the point of shorting out. The only K3706 I have found are from china and would take weeks to get here, any common equivalent available? or what to look for to find a good equivalent? What can I look for while I am waiting for parts to help identify on why it shorts out. NOte that I also found Q7505 (P/N J655) next to it also shorted out.
I have attached pictures of the board, note the problem mofset is removed

[R_J]

I thought you were still repairing the power supply, I see you are now repairing the backlight inverter.
If the mosfet was shorted D or S to Gate, then the drive components or drive ic is likely bad as well.
Q7505 might have been damaged when Q7506 shorted.

[Plane Nuts]

Yes both Q7506A and Q7505A were both shorted out between the three Pins (S, D and Gate) so what would cause it to short out like that?