"tried pushing the 'pwr on' button on the motherboard" ... I'll assume u mean the red micro push-button in the lower right quadrant, if so then that settled that

The fact your mthrbrd tell-tale LED goes off / turns on after removing / applying wall-cord power is a good sign 

***In the steps below, if I say to 'turn system on', u may use the top external button, the on-board red mini power button, or later see a way to 'jump start' system on directly at the front panel header

Were this my system here, I'd start by uncoupling then recoupling the 24pin ATX connector, located at the top right area of the motherboard (a rectangular white connector with multi-colored wires). When it is decoupled, inspect it for bent damaged or backed-out terminals & take a close look at the single green wire also since that is the wire that turns the system on (known as pin 16 / PS_ON, see detail in photo). If system wont turn on after inspecting & reseating the white 24pin, see below

Power supply (PSU) & case harness can detach > decouple the black 66pin bulk connector from the PSU (see photo), if u have hand room to grab the 66pin then it won't be necessary to touch the PSU or rear handle, just make sure rear handle is locked in place then decouple the 66pin (squeaze the pair of plastic side-tabs then back it out) > I'd inspect the visible metal PSU terminals for bent damaged or backed-out pins etc, where if even one of them looks 'different' (one relative to the next, where a pattern of what are 'normal' / good pins inside there 'should' look like) could be the reason for a non-start. If a pin is backed-out, reinsert it ... if it backs out again (after recoupling 66pin to PSU) u may need to take a micro-tool & re-set the terminals retaining arms so it locks back in place

If all looked ok in the front & back of the 66pin & you reseated it so it locked back in place (side tabs clinch in place), & that didnt help start the system, I'd disconnect all items from the PSU

1) Eject all Hard Drives from the hard drive bay

2) Disconnect all items from DVD area (DVD/Card Readder/Floppy etc)

3) Disconnect from motherboard the 24pin ATX (top right) & the CPU 8pin (top left),

4) Remove video card(s)

5) When all hardware items in system are disconnected from PSU power, take a metal-tool (normally a 'paperclip', or staple, or jumper wire), take the 24pin ATX white connector, find pin 16 GREEN & find a BLACK wire GROUND (pin 15, 17, 18, 19 etc) & jump start the PSU on by bridging (shorting / jumping) pin 16 to a black ground. If PSU CAN be forced to turn on (the PSU fan turns on, the rear green LED lights up), reconnect all your hardware & PSU connectors to system & retry your power button etc to see if system comes on

If it won't, try to jump start motherboard on directly at the front panel connector, see uTube

If it won't, try the PSU self-test (uTube)

How to Run a Power Supply Unit Self Test On a Dell Desktop or All-in-One Computer