Dunno if it’s poxy solder or cheap manufacturing or what, but if I were a betting man I’d be leaning towards inadequate cooling.
I think that’s related though, once upon a time, the solder would have coped, now it seems more fragile under those conditions.
Where can you find a laptop with decent cooling anyway? My Macbook, MBP and top end HP laptop all run red-hot when viewing youtube or other CPU heavy tasks, so hardly surprising that mid-range models such as the Inspiron series will suffer too.
Back to the OP, if Dell won’t touch it, the reflow they talk about in the link earlier in the thread is worth a shot, otherwise flog on ebay for spares or replace the motherboard.
As Cougar says, unlikely to really be the CPU which is busted.