While auto transmissions are not my high point, as far as I know, the first good thing about this problem with the flashing S light, is that it indicates an electrical problem with the A/T and not a mechanical one.
When the A/T control unit senses an abnormality in the input or output systems, the "S" indicator light will blink.
You can jumper the Service Check Connector, located to the lower right of the glove compartment, and the "S" indicator light will blink the problem code when the ignition switch is turned on.
Problem codes 1 through 9 are indicated by individual short blinks, Problem codes 10 through 15 are indicated by a series of long and short blinks. One long blink equals 10 short blinks. Add the long and short blinks together to determine the problem code.
The Check Engine light has to do mainly with emissions, it could be any number of things from an oxygen sensor needing to be replaced or the gas cap needing to be tightened down. Again, you need to jumper the connector under the dash and get the code and find out what it's telling you.
The speedo not working is usually the speed sensor needing to be replaced.
These are just the first and most common answers to these very generalized questions. If you have more detailed info, I might, or someone else might, be able to get your more specific answers to help you figure out what's wrong.
I'm not sure where you are, assuming in the UK, but If you don't think you can perform the self-diagnostics yourself, then I would recommend taking it to a Honda Dealer and let them diagnose and repair the problem (the most expensive answer) OR -- if you have auto parts stores there like we have here, places like Auto Zone, etc. you can take the car there and ask them to read the codes and they will check your system (they do it for free here) and give you a print out as to what codes your computer(s) are throwing and what those codes mean.