Before you blame the mainboard, check the BIOS setup. Is the AC adapter listed, or is it listed as "unknown"? If it's unknown, try another Dell adapter - and if that doesn't solve the problem, replace the power jack (see below).
If neither of those solve the problem, it could well be the mainboard - but since that's been recently replaced, it's unlikely - far more likely is that it's the adapter (about $35) or the power jack (about $20).