m15 R5, doesn't work with HDMI adapter when it's powered

You may want to contact the adapter/charger manufacturer for support.  Usually, the adapter, charger, and cable are made to support the devices.  Not the other way around.

Which specific Alienware Laptop?

@Chino de Oro​ yeah, well, that's what I originally thought. I thought the adapter or the charger was the issue. However, 
* I tried half a dozen USB C PD chargers, ranging from 30W to 100W, from manufacturers like HP, Dell, Apple, Anker, etc.
* I also tried two adapters, from Monoprice and Acer, with the same result. These two adapters work fine with the other PC I mentioned.
* I also tried at least 10 cables, all good quality 100W cables with proper e-markers (I tested with a PD voltmeter)

So I suspect the power routing broke down between the laptop and the adapter. I wonder if it's a bug in the Alienware's firmware.

@DELL-Chris M​ 
Alienware m15 R5 Ryzen Edition

The adapters:

https://www.amazon.com/dp/B0B2ZZJPM3

https://www.amazon.com/dp/B0CQT3CPPZ

So you are saying that the provided  D0X04 Liteon 240W barrel AC power adapter is plugged into the rear of the m15 R5. Then when you connect any of these USB-C to multiple port adapters, the HDMI on those doesn't work?

But if you disconnect the D0X04 Liteon 240W barrel AC power adapter, the HDMI port on those adapters then works?

Since OP only described in general for connection setup and disclosed very little details of the devices and powers being used with the connections, I could not be certain but here is my thought:

OP was trying to connect the m15 R5 with PD port from those adapters and of course the power delivery of 65w (from non-Dell power source) being detected as too low and not to be accepted by a 240w m15 R5.  Therefore, it triggered POST error message at boot about the status of low wattages detected.  By using the adapter, an external monitor must being used (connected to HDMI) and external monitor could not displayed the POST error message.  Until OP removed the power delivery and the m15 R5 could passed POST and provided display signal to the external monitor. 

Conclusion, if my guess is correct, there is no issue with he m15 R5, it works as designed.

I'm not using the 240W barrel AC power adapter at all. I am not trying to charge the laptop. Here's a diagram of the connection:

M15 R5 USB C <-> Adapter ---> HDMI monitor
                     ^
                     |
                     +------- PD power source

The HDMI adapter can pass through charge the host if it supports charging through the USB C port. My understanding is that M15 R5 does *not*. It only charges via the 240W barrel AC power adapter. But I expect the HDMI adapter to work regardless.

However, when the PD power source is present, the HDMI adapter doesn't work at all. It doesn't appear in the device manager. But if I disconnect the PD power source from the HDMI adapter, its HDMI function starts working again.

And since it behaves this way with two different HDMI adapters (listed above, one Acer and one Monoprice), I suspect there's a bug in the M15 R5's firmware.

@Chino de Oro​ thanks for the diagnosis. here's a few clarifications/questions:

1. I am connecting everything while the laptop is running, not before booting. So this should have nothing to do with the POST message.

2. Does M15 R5 charge through the USB C port at all, if I provide a 48V 240W power source (maximum wattage spec'ed by USB)?

3. If so, my understanding is that it should also be able to draw from a power source of lower wattage, at a lower rate, right? I thought that was required by USB specs.

4. Regardless of the power negotiation, I'm baffled why HDMI doesn't work. I'd expect it to be independent of charging. 

I think you understood my explanation.  There is no bug, the firmware works as designed.  The PD addition on the adapter was the issue.  It halted POST when detecting any outside parameter power threshold.  Take that (power delivery) out of the equation should resolve HDMI display  issue.  Which it did.