Look for the presence of green slime on the dipstick. I had the same problem and found that the black plastic filter nozzle at the outlet of the washer bottle was gummed up with the stuff. It's probably caused by a cheap and nasty screenwash that's rather too organic and has caused/let bacteria grow.
To access it, it's a bit of a game. Jack up the front left of the car and remove the wheel. Remove the plastic inner mud shield with two TORX-25 screws and a few plugs. The plugs are removed by pressing the centre pin through, then remove the plug and retrieve the centre pin. However, don't do this on the very back one because it disappears into the body!
Once removed, you can get to the bottle. Remove the motor by pulling upwards in line with the bottle, then pull outwards. Then remove the bottle with two 10mm screws, one is right at the front and a bit tricky to get to. Remove the bottle and clean it out thoroghly, including the black rubber filter that just pulls out. Then replace it all and fill up with water. It may need a bit of coaxing to prime the pump - pulsing the spray seems to do this best.
I also unplugged the front windscreen wipers before playing with it, so they wouldn't be wiping on dry glass. The plug is a wide one under the bonnet just in front of the steering wheel.
Good luck!
Clive Miller, January 2006