Originally Posted by
Ed Oscuro
If it has a PC VGA port (31KHz scan rate) you should be able to use a VGA to component converter. HDMI might be possible but might need to be converted to PC VGA as an intermediate step, depending on what devices are out there. It wouldn't provide any benefit over VGA anyway. If your laptop is slightly older it might be possible to connect it to S-Video right away (look for a S-Video-like connector on the back, looks like the PS/2, pre-USB mouse and keyboard connector).
The next thing you'd want to do is set the output resolution low; it might take some fiddling to get it looking nice. If this is Windows 7 you might not be able to set it low enough to look really right (Powerstrip maybe?) but it's worth a shot.
Going from the progressive scan to 480 lines interlaced can be a challenge but hopefully it'll be fine for emulators. Text and other stuff in Windows might not look so crisp; there might be shimmering also.
By the way, use some q-tips and 99% isopropyl alcohol on the cartridges...and clean the SNES itself or try another, because the console's connector sounds like the culprit. Most SNES games shouldn't just stop working.