If it doesn't POST, it could be a myriad of things, most of which couldn't be troubleshooted without specialized equipment and the PCB schematic, of which is proprietary and isn't available to anyone outside of Dell. However it's best to start with Occam's Razor (the most likely answer is the simplest), and work up in complexity.
I would start by disconnecting all peripheral cables from the MB (i.e. HDD cable, CMOS battery, ODD, etc.), except the keyboard, mouse pad, video, and fans.
This is to rule out a few things:
A damaged peripheral or cable, as if the PCB is getting power and not POSTing, it's likely not doing so for protection due to a damaged component, damaged cable, or improperly seated cable.
An improperly seated cable can cause a system to catch fire, and if the PCB detects a short or open circuit from an improperly seated cable, it will refuse to boot.
Check all cable lock tabs, as if one is damaged and not securely holding a cable, it only takes a cable minutely seated incorrectly to cause one of the pins to cross and short circuit.
If it doesn't POST, remove all RAM modules, then reinsert 1 at a time and try to boot (rules out a bad RAM module, which can cause a system to not POST)
You'll know you're making progress if it beeps during POST, of which will allow you to further diagnose it from the amount of beeps.
You may want to look into whether or not Dell could repair the MB, of which is likely a few hundred dollars for the repair of the PCB.
Keep in mind you can also buy a used MB on eBay or Amazon for ~$300, however, it will vary wildly depending on the seller and supply and demand. I've seen used M18x R1/R2's MBs as cheap as $275, and as much as $450.
If you choose to go this route, first call dell and find out what they charge to repair a system out of warranty, and how much they would charge if the motherboard needed to be repaired (it's likely in the ~$300 range)
Dell does refurb their MBs, however I'm not sure if they do so for a customer repair (i.e. if a PCB component is damaged, I'm not sure if a customer can pay to have them simply repair the PCB, or is it simply a flat fee to replace the MB with a refurbed one, at which point they keep the damaged PCB, refurb it, then put it back in circulation)