I had the same problem mate, if its the same thing as what happened to me then fuse 15(ithink) will be blown? Means that your alternator wont be charging the battery either as its on the same fuse somehere along the line.
Took me ages to find out what this was i nearly went insane. Was a short circuit where a wire rubs on the intake manifold bracket. Get the car on axle stands and look from the bottom of the engine bay up at the rear part of the engine below the IM, there should be a pack of wires right next to the bracket if you have a good look theres probably an exposed wire shorting out, just wrap it up in a bit of electrical tape and job done.
Im almost certain thats what your problem is, good luck.
Ok im now almost 100% sure that its the short circuit thing, and if it is the alternator isnt faulty it just isnt charging the battery because the fuse has blown (15) from the wire shorting out on the intake bracket. Which for some reason is also the fuse for the speedo which is why your speedo dont work either. Trust me have a dig about in the wires behind your intake manifold and youl see what i mean all it needs is a bit of insulating tape