Well just tried again at ILS18c Schiphol and same thing happened. It seems to turn way too early. G/S showed up when I had the "LOC" button pressed but when I tried to press "APP" it wouldn't switch on. Frustrating stuff!!!
I did manage to take some pictures to see if that helps.
http://s4.postimage.org/h2vnpo0dl/approach.jpg
http://s12.postimage.org/4b54ne3h5/approach1.jpg
]http://s4.postimage.org/wea240n3d/approach3.jpg
I'll admit I've only skim read the answers after this post but I couldn't see anyone pointing out the obvious problem. Your final is waaaaay too short. You're setting up for a ~5nm final when you should be looking around the 15-20nm mark. As a result, the Glide Slope is coming in before you are on the localiser and the autopilot wont play ball with that. You should be well and truly established on the localiser before the glide slope even pops up on the screen. The cause of this is that FMC STARs don't really cover the actual approaches, they're supposed to just get you into the vicinity of the airport. As mentioned earlier, in reality at some point you would either follow a procedural approach plate (but I won't go into that here), or be vectored by ATC to the localiser, with an example I made from your screenshot as shown:
http://i49.tinypic.com/2zs4itz.png
This should set you up for a nice long final. If you're just simming offline then you'll have to judge it/fly it a bit yourself with the map in FSX and the DME readout.
I did a quick mockup to try and explain. Note that I have already descended to 2000ft and slowed to 180kts (to match your screenshots). However flaps 5 is better here, 15 is too much. Here's me after all my imaginary ATC vectoring and am shortly about to be closing in on the localiser from 18 miles out:
http://i47.tinypic.com/effg3q.png
Once you're on that final vectored heading (should be about 30 degrees off the final track, in this case 150), now is the time to hit the vor/loc button. On the top of your PFD (primary flight display) you should see vor/loc at the top in white, meaning that its armed but not active:
http://i45.tinypic.com/35jf8uc.png
Soon the localiser should go from an outline to a solid magenta colour on the ND (navigational display) and start moving in and as you've been seeing. This is often referred to as 'localiser active':
http://i49.tinypic.com/2ai3e3c.png
Once its about halfway from the edge to the center (called half-scale deflection), the white vor/loc text should go green, meaning its now activated and the plane should line up with the localiser (hdg select will automatically disengage):
http://i46.tinypic.com/2v0nbj4.png
If the GS starts moving down at all before any of this then you're still too close and you should try again. You can see from the next screenshot i an lined up with 10nm to go:
http://i45.tinypic.com/2pynlaq.png
Once you're sitting on the localiser and stabilized you should hit the APP button. Again on your PFD you should see G/S in white, once again this means it is armed and waiting for the GS to come in:
http://i47.tinypic.com/6pxn3p.png
Once the Glide Slope becomes 'active' you should drop the gear and set flaps 15, once the GS is at half scale deflection you should go flaps 30/40 and set your approach speed (usually weight/flap setting dependant but 145kts is a good ballpark figure). Also arm your spoilers and set the autobrake if you know how. Once the GS is close to centered, the white G/S goes green, Alt Hold should disengage and the plane should follow the GS. All of this happens quite quickly but with bit of practice and each step flows nicely into the next. Only downside is that I couldn't take separate screenshots so this ones a bit busy (note that I still have 6.5nm to go and have only just got onto the GS):
http://i49.tinypic.com/2nr5ah.png
If you want it to actually land by itself, now is the time to engage the second autopilot. If not, then you should disengage the autopilot/throttle at 200ft above the ground at the latest and manually land it.
http://i45.tinypic.com/wv4v2r.png
So, in summary, autopilot ILS - make yourself a much longer final and make sure to get on the localiser first before the GS, otherwise it spazzes out!
Pictures changed to links due to image size.