Check the basics first - are you doing anything specific when the smell gets more noticable? IE playing games, which stresses the CPU and HDD, or compliling a mahoosive DB which would make the HDDs run hot as they thrash data. If so, check around the components likely to be stressed for any contact with anything that wouldn't like heat - braiding, cables, etc.
I'd start by getting a few zip clips, a can of compressed air and doing a dust-clear and cable-tidy mission - it will take a while, but if you can get all the various parts away from each other then you can rule out component/cable interference -IE a fan cable resting on a GPU heatsink or something, dust bunnies/dead insect stuck between the edge of a heatsink and a PCB - I once saw a dead spider wedged inside a Socket 775 heat sink, when the heatsink heated up, it started to reek. Blast of compressed air cleared it out, no more niffyness on load.
Also, any components you can disassemble, do so, but be wary of warranties. IE, is there some paper stuck inside the GPU heatsink? Are all the power connectors firmly in place, so there is no arcing [which is extremely unlikely, but not impossible on high load devices like GPUs] or something else.
Strip everything down as far as you can, clean it out with compressed air [NOT a vacuum cleaner] and give everything a physical once over - check for blown/expanding capacitors, which can smell fishy, or general detritus in areas of heat buildup.
A blow cap looks like this, by the way - image found on another forum that isn't an OCUK retail competitor as far as I can tell:
The caps at the top of the image are OK - flat tops. The ones notated are what you are looking for. Caps can smell before they visible leak, but normally if they are going, they will be noticably expanded at the top, as per the image.
Incidentally, it's never too new to be dust - it just might not be dust. As noted above, insects aren't uncommon to find in PCs. Hence I will say again, get some compressed air and clean everything as best you can.
I'd also kill as many fans as you can and then run them one at a time -take the side panel off your system and lay it on it's back first, obviously, so that it doesn't overheat. Let each fan run off a 12V molex connector [for max speed] and see if you can smell anything from them. Try and do similar [if sensibly possible] for the CPU and GPU fans, if you can.
That's about all I can think of. Hope that helps.