Check the crystals. If you have access to an oscilloscope, you can probe one of the pins of the crystal and you should see the oscillations in the frequency specified on the schematic. ( Yes, it's the same schematic you linked you. Apparently, they don't allow direct linking)
However, that's a really wierd failure scenario for a SNES. I've repaired _tons_ of them, and haven't seen a "slow" SNES ever. Plenty with the black screen, but I don't think any of them had sound either.
Anyhow, I'm hoping you did the obvious things before jumping to caps? As in, cleaning the cartridge connector, as well as lifting it up, and cleaning the connector-to-the-connector (or whatever it's called). Some might require re-tensioning of the "blades" in the connector as well, depending on how its been used.
This easily fixes 9 out of 10 SNESes that passes by my desk..
Also, verify the output from the 7805. I've seen a few of those go bad as well, and cause wierd and wonderful failure modes.