Field IC is burnt Lg 29FG1RG - LG Televison & Video

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Free schematics are hard to come by, I can find the service manual for these sets but it doesn't include schematic diagrams, you can purchase it here and download both them but they cost about 20 bucks each. Another option is contact LG and request the manual, most manufacturs will offer them for free
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What you can do since there aren't any schematics available, would be to measure the 1 half and write down the resistance and do the same with the other half and add them together. You should go up a little also, say if you are reading 1 k ohm, use a 1.2k ohm in it's place. The other way is to follow it upstream to see what the resistor is supporting. If it's an I.C. you could look up the I.C. number and go to website to see what resistor is required to support that I.C.

See here:

http://www.archivotecnicosaurios.com/descargas/tv/seccion_ordenada/12950_Chassis_CW-62C_Ver_2_Manual_de_servicio.pdf

Monitor horizontal lines problems usually caused by a defective vertical output/driver ic. A missing supply voltage to the vertical output ic may caused similar faults which is one horizontal line across the display. Dry joints and missing vertical output pulse from vertical oscillator ic also could contribute the same symptom. If you discovered that the protection resistor (usually from 1 to 4.7 ohm) open circuit or burnt, then replacing it won't solve the problem. The resistor burnt or open circuit was due to a short in the vertical output ic. Thus you have to replace the vertical output ic and the burnt resistor together before you switch on the monitor.

The field is notorious for failing in these tools -
If you remove the cap on the field housing you can access the field wires - check to see if you have continuity through the field windings.
To further investigate
1) Remove the brushes and inspect them for excessive wear or chipping (If they look burnt or are chipped the armature is suspect)
2) Remove the 4 screws holding the field assembly to the saw frame
3) Pull the field off and inspect the armature (especially the commutator (copper segments the brushes ride on) for burnt or raised segments or windings.

Surprised to hear that the HDMI input connector is burnt, however have you tried another HDMI port? If none of the HDMI inputs are working then a software updat could fix it or the HDMI switching IC maybe at fault. If you get a picture from the spare HDMI ports then the faulty HDMI socket can be replaced by an engineer.

What is the Brand name and model number to your TV?

relay problem