If the CPU is a Gen1 Intel then u have an R1, not an R4 (for anyone reading this, see
Wiki/Alienware for an R-version breakdown, which means the Generation of Intel CPU in the motherboard dictates its R or Revision #)
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You were correct to try & 'short' / 'jump' the Front Panel pins 6 & 8 together in an attempt to bypass the top external power on button; if the desktop did not turn on, PSU will not turn on, I might remove all memory, unplug/remove video card(s), unplug MIO board 4pin power, unplug Hard Drives, unplug items from DVD bay area & then attempt to short pins 6/8 together, see what happens > if desktop turns on, kill power to it, plug-in MIO board & retry
But if no joy, & if the rear
PSU Built In Self Test button (ie Green LED) 'works', I'd unplug the 24pin & CPU 8pin cable from PSU & ATTEMPT A
JUMPSTART of the PSU itself (paperclip method) by shorting/bridging/jumping pin 16 (green) w/a ground (black) pin 15 or pin 17 etc in the 24pin section, see if PSU & PSU fan comes on, ie prove PSU can turn on by itself, it will or won't
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If PSU does turn on, then plug 24pin & CPU 8pin back into motherboard & retry to start (ie bridge Front Panel pins 6/8)
If no joy, and if new motherboard is on the way, I might bench test the 'old' motherboard by removing it from case, remove PSU & the 66pin case harness, put it all on cardboard, insert the 24pin & CPU 8pin, bridge pins 6/8, see if it turns on (ie motherboard fans come on, PSU & PSU fan comes on) … if it does turn on, kill power & report back … but if no joy during bench test, culprit is CPU, motherboard, or both, so long as the coin-cell battery is new & inserted correctly
Note, that if all memory sticks are removed, motherboard should 'beep' when power is applied … if power is applied & no beeps happen, most likely = mthrbrd failure
From there, when new mthrbrd arrives = a good time to bench test it before install, so, put it on cardboard, transfer your i7 975 into it, plug PSU 24pin & CPU 8pin into it, bridge pins 6/8 & see if it turns on (if no joy, replace the coin-cell battery with your new one & retry) …
From there, new motherboard either will or will not turn on > if it will turn on, it should beep because there is no memory sticks installed, so kill power ot it, insert one stick of memory & power it back up … it should simply turn on
If it will not turn on with or without memory, then we'd suspect the CPU … but! … given that the R1 desktop PSU is over 10years old, maybe yoiurs is shot/old … therefore you'd do well to benchtest with a different PSU, see what happens … if different test PSU fails to power system on we'd suspect the CPU is toast … therefore, u might invest into a cheap i7 920 to test with
As for a new aftermarket motherboard, anything from say an Intel 8700k era chip to anything newer will blow away your i7 975, which is to say you can stll maybe put in new hardware & not break the bank, knowing new hardware means u invest into newer DDR4 memory also