The most common cause of the "continuous" running pump motor is the shorted Triac that Bill showed the picture of for the Gicar 3D5 board. You can tell if the Triac is shorted if the pump runs immediately. The microprocessor takes a second or two to reset and go through it's initial steps. If the pump runs immediately it is doing so uncommanded which is the signal of a bad component.
The Triac is rated at 6 or 16 amps depending on the vintage of the board. The problem starts when the pump gets tired and the runup time for the motor increases and the inrush current causes overheating of the triac. This causes damage to the triac and decreases the ability of the triac to block voltage. Eventually the triac will fail shorted and the motor will run constantly. The problem is that the triac often will not fail catastrophically but will degrade with continued use. It is during this time that the triac is blocking some voltage. With a voltage drop at the triac it starts to generate heat (Ohms law). I often see the board charcoaled or blistered from the triac heating. So one asks, "how come the fuse didn't blow?" The fuse should be 6.3 amp slow blow fuse. Fuses work by heating and then melting. It takes a sustained current draw to make the fuse blow, such as a shorted wire would do, rather than inrush current.
Often the triac will take on a pretty blue hue which is an indicator that is is getting hot when used.
Soldering is easy, de-soldering is the tricky part. I have a pile of 3D5 boards that have been hacked with a big black Weller gun and the copper traces are peeled up off of the board. I was able to fix some but others are now dead players. Boards are easily repairable at considerably less money than a new board. Bottom line is you have to figure out what is causing the triac to fail. Triacs don't wear out like relays so usage is normally not an issue like a relay that has physical points that erode from arcing.
Interesting posts as I have been researching ways to economically measure the inrush duration to be able to tell a stand owner that they need to be thinking about replacing the pump before they need to add a control board to the order. LaMarzocco Swift grinder power boards often suffer from the same scenario.