The other guys are right. You can usually fix that by carefully cleaning the cartridge slot and sometimes the connector edge on the actual cartridge itself. Also do a visual inspection looking for bent or damaged pins on the edge connector.
The noise is because the SC-3000 doesn't have a BIOS or ROM on-board. It can only execute code that it sees at the cartridge slot. By default, when you turn the SC-3000 the sound chip emits that 'humming sound', and the SC-3000 has to execute code from the cartridge to turn it off.
If cleaning the cart edge doesn't work and you are confident working inside the computer, then this is how you open it:http://www.sc-3000.com/index.php/How-to ... board.html
And here is a schematic. This was scanned by natshaw, and I think the original came from radar, both from the classic computer forums.http://www.sc3000-multicart.com/images/ ... tic_A3.jpg
If you do open it up, the problem is still likely to be somewhere around that cartridge edge connector because the fact that you are getting that black screen and humming noise suggests the unit has power and the video RF circuitry is working. Check the solder on the underside of the edge connector. If the glue under it has come loose then some of the joints might have cracked.
Aside from that, I haven't seen any CPU failures on SC-3000s. I have seen VRAM chips and SRAM chips that needed replacing. And natshaw managed to fry the VDP one time
You can replace all those if necessary, but focus on the cartridge edge connector system first.
Also check the voltage levels coming off the voltage regulator is 5v as I have seen one of those go bad before too.