Hi
Here's my basic understanding of it, however limited it may be (I'm also seeing this thing for the first time).
C1807 and C1808 form a series capacitor, with the 10M resistors for balancing (to prevent one of them from being overcharging by random leakage currents), so you can treat the whole C1807-C1808-R1817-R1818 thing as just being one 15 nF capacitor with a double voltage rating.
This compound capacitor, together with the T1801 transformer's primary forms a resonant LC circuit. Being resonant, this LC must be working with a waveform that closely approaches a sine wave (in contrast with typical switcher waveforms that are more square-like).
Now the whole thing in line between V1806 and T1801 is basically a power square to sine wave filter. V1806 is driving a square wave (being a switching transistor it can't do otherwise), so it takes some filtering to make a sine from that.
The main part of the square to sine conversion is probably done by L1806 (the primary winding of it, the one on the lower side in the schematic). Together with L1804, L1806 serves the same purpose as the series inductor in the classic Baxandall converter that is used in resonant CCFL drivers.
Like in the Baxandall, the inductor sees a square wave on one side, a sine wave on the other side, and eats the difference. The waveform on this inductor therefore looks like some sort of arithmetical difference between a square and a sine.
Only in contrast to the Baxandall, which uses a push-pull topology where one of the two switching transistors is always on, in your power supply, the V1806 transistor only provides conduction during one half cycle. This leads to the necessity to discharge the energy stored in L1806 during the other half cycle, during which the transistor does not conduct (in the Baxandall this part is handled implicitly by the other symmetrically arranged transistor coming on as soon as the first one turns off, but here, there is no second transistor). Therefore a secondary winding is provided in L1806 (the upper one on the schematic). This is a reset winding, and its function is to reset the field of L1806 during the off-cycle time. In the course of the reset, the stored energy is circulated back into the primary capacitors C1802+C1803 through the steering diode V1811, which thereby forms an energy recovery circuit.
Now because there is still some leakage inductance between the windings of L1806, there remains some little energy stored in the leakage inductance that the energy recovery circuit cannot recover and that would otherwise end up creating huge voltage spikes at turn-off. This energy from the leakage inductance is dissipated in the RCD snubber circuit formed by R1816, C1806 and V1809. The snubber eats the spikes in the capacitor C1806 and slowly dissipates their energy in the resistor R1816, thereby keeping the inductive transients of L1806's primary at bay.
Note also that L1806, together with its upper reset winding serves an additional duty as the power supply's overload protection. Should the main transformer (secondary or otherwise) for whatsoever reason become overloaded or shorted out, then L1806 becomes a current limiting element (like a fluorescent light ballast) that circulates energy back and forth from the primary capacitors and back to them. This runs the switcher at maximum rated current, but safely sends the energy back into the supply, preventing the switching transistor from overloading.
Now, for whatever reason, the power supply's designer must have figured out that L1806's inductance alone was insufficient to cleanly convert a square into a sine wave. Maybe L1806 has a little too much interwinding capacitance, and therefore it has ended up less efficient than desired when it comes to filtering the high frequency components (the steep rise times) of the switching square wave. So the designer has added L1804 in addition (likely making it smaller and of a construction with higher self-resonant frequency, at least that's my guess). Now this winding, too, needed a reset, but either the energies involved would have been much lower and/or possibly the reset did not need to be complete and significant DC field is allowed to remain in L1804 on average, so the designer chose to provide no energy recovery but a dissipative snubber instead, and made that snubber from V1808 and R1814.
L1804, having no way of energy recovery, is probably not directly involved with overload protection, but still, in the event of an overload, when the energy transferred over L1806 reaches its maximum, L1804 would also see both maximum average currents and maximum peaks.
Therefore, since the peaks are being dumped into R1814 for resistive dissipation, the fact that R1814 heats up too much, especially if there is no load on the outputs, could be an indication that something is overloaded down the line (in the main transformer or later) and the whole thing is operating in permanent overload protection mode. In this mode the main transformer would be out of resonance and L1806 would be circulating a lot of energy back into the input caps. Now what is really responsible for the overload is another matter, but it could be anything either in the main transformer itself (winding is suffering a dielectric breakdown, shorted or arcing) or later on (output rectifiers or output filters). Can you check the main transformer's waveforms for evidence of dielectric breakdown? (Careful with the high voltage!) If some isolation breaks down, the waveform would be unlike a sine wave, and would likely show places where the voltage "just drops for no reason".
Note that there are many guesses above, wild or otherwise, so please take my description with a grain of salt and, anyone here who happens to know more details, please correct what needs correction.
Dimitrij