I've tried grinds from a very fine to a coarser grind in my Rancilio Silvia, but the water is going through the portafilter/coffee too quickly. When I clean out the portafilter, there is too much dry coffee in it. I've cleaned it.

First, I'm not a Rancilio tech but I have worked on similar models.
*** All service should be performed by a qualified technician. The following is for information only ***
* Usually one gets less water out of the portafilter rather than more (or faster). Check the amount of water on an empty shot. It should be between 1-1/2 oz to 3 oz (depending on your shot size) If this is a manual on/off shot then disreguard.
* Fast pour is directly related to the pressure setting (usually 9 bar), Coffee amount, Grind size, and Tamp (or compression). You can check most of it by following the many examples given on you tube. Water pressure is a bit harder as you will need a pressure guage portafilter.
* If your still having problems with fast shots then have your service vendor check and adjust the bar if needed.
Aloha, ukeboy57
P.S. Check if your using the right portafilter, There are many types used for different purposes; Pod, Capsule, Single, Double, Tripple, Drip coffee (Americano), Back pressure adjustable, ect.

It is possible that the grind you are using is too fine and causing so much back pressure that the portafilter is moving, also possible that the group gasket installed need to be replaced, I have also seen this happen with damaged screens.

starter on 2008 ford edge location

try making your grind a little bit coarser. this can happen if grind is to fine.

The group gasket is either dirty, or there is some damage on the basket of the portafilter that is letting the water flow.

Try to redo what you have been doing, but set it to the extremes to see if everything is functioning. If you set the grind say to 4, it should come out very slow or maybe not at all.

Try backwashing the group with purocaff.
Are you using coffee ground at the store or do you grind just before use?
How fresh is the coffee less than a month or more?
If more than a month(whole beans) it is no longer useful.
If more than a 3 days(ground), that is stale also. It will be very diffucult to get good espresso from that(not impossible, but difficult).

If using store ground, it cannot be ground older than a week(coffee loses flavor and taste minutes after being ground). Try getting less coffee more often and adjust the grind setting that you use. If you have always used setting 3 on the store grinder try 2.5.
If grinding at home adjust the settings on the grinder to a slightly coarser grind and fill the portafilter slightly over the top of the basket, now tamp to the indent(fill line) in the basket. that should be sufficient to pull a great shot.

Try taking the portafilter out and run water through it as if you were making an espresso. check if the water coming out is very fast. I believe there is a screen there that is held in by a flat screw. If you take that off you should be able to see light through it. If you can't soak it in some cleaner until you can see light through it. There could be a couple of things causing this. The other thing that comes to mind is that the boiler has to much pressure but it should say on your gauge if that is happening. You might find that it just needs a good cleaning.

1. check the coffe filter>> it could be teard up and leaking(check it carefuly it is hard to see sometimes)
   
2. check the pressure you get from group. 7 - 9 bar pressure you should get to handle. if it is biger than check by pas valve and adjust the pressure, also check up boiler security valve(security valve for water for coffee)
   

How long does it take to fill the cup?
Sounds more like too coarsely ground espresso to me. Should take about 25 seconds for 30 ml of espresso to come out ... that is normally more like a 'trickle'. If yours comes much faster, you might try grinding it finer and/or tamping more firmly.

Best regards,
Andy