The Rancilio Silvia is a hugely popular home espresso machine and there are loads of them out there. One of the more common troubles that can occur is a clogging of the 3 way solenoid which causes the machine to stop dispensing (making espresso).
To properly diagnose the problem you must first eliminate the other possibility which is a failed pump. Luckily this is super easy to do. With the machine plugged in turn the steam knob counter clockwise to the open position, turn the machine on and turn the middle switch at the left side of the panel - below the coffee button - to the on position. At this point the pump should come on and within a few moments water should start dispensing from the steam wand. If water does not dispense from the steam wand you will most likely need to replace the pump (a subject for another blog post).
Most likely the water did dispense from the steam wand which means you probably don't need to buy any parts but you will have to do a little work.
FIRST UNPLUG THE MACHINE
The problem you are experiencing is a blockage of the 3 way solenoid valve. This part is located behind the brew group and drip tray so start off by removing the Portafilter & Drip Tray.
Step 1. Remove panel screws:
Step 2. Panel is removed by moving to the side and angling it as needed.
Step 3. Remove Black plastic jet breaker - Use a pair of pliers and carefully turn counter clockwise.
Step 4. Loosen the nut that retains the coil with a 14mm wrench.
Step 5. Remove the coil from the Solenoid shaft and let it hang on the side.
Step 6. Loosen 2 allen screws with 3mm allen wrench. Be careful that the rear one does not fall through the hole behind where you are working.
Step 7. Firmly pull the solenoid valve off.
Step 8. Looking at the base of the valve you will either see black gooey coffee stuff or mineral stuff. You might not be able to see it as the blockage might be inside of the valve. In this case there was gooey coffee stuff visible from the base.
Step 9. Use a 22mm Wrench to remove the shaft from the base of the solenoid valve so that you can clean it thoroughly. You will need a larger wrench, pliers or a vice to hold the base steady while removing the shaft.
Step 10. Soak in a solution of hot water and Pulycaff or other back flush solution. Scrub with little hard brushes if you have them.
Put it all back together with clean solenoid valve - Basically trace the above operation backwards. Be sure to install the solenoid valve in the same position so that the 2 holes match with the holes in the group body - other wise you will have to do this over again. If you do this operation and the unit still does not flow, you may have a failed coil (rare) or more clogging inside of the boiler (also rare).