Screwdriver across which terminals? There are 2, one smaller spade terminal for the starter solenoid (that usually makes the click) and one big one for the starter which goes off via a chunky cable to the battery with thinner one off the same terminal to the alternator. I'm not sure if this is the same as your problem but the symptoms I had were pretty much the same for me on Saturday, I've always managed to start my car (8v) since I got it back in April but the starter has always seemed a bit sluggish, even moreso since the cold weather, even with a new battery. it would just about turn the engine once over but somehow started, anyway, on Saturday I went to start it 1st thing, the engine did 1/2 a turn, then nothing, just click,click,click. I figured I was in for a new starter, I checked the connections on the starter and all 'looked' fine, but when I tugged at the heavy cable it came away leaving the circular connector on the starter, it had corroded right through............so no current getting to the starter. I got a new thick cable from Halfords (£5) and connected it (with a bit of butchery) and hey presto I now have no problems starting, the starter spins the engine over easily now even sub-zero and the battery charges up quicker. (the smaller wire from the alternator runs through the thick wire to the battery so with an ultra thin corroded connector hardly any current was getting from the alternator back to the battery I guess). I hope your fix is as easy as this.
By the way, if you're getting the 'click' from the starter motor then the problem is not with the ignition switch or relays. Check all the earth cables as well, especially the one to the gearbox.
