You should be able to open the Z-controller via 4 Phillips screws. Takes just a minute.
Once open, I figure it will look like this - a Z-750 controller but it ought to be similar. Front and back:
It's not clear to me if you absolutely must remove the aluminum heat-sink plate to access the 3-pin triac (circled in red). But if so, that requires unsoldering the 3 wires going to the adjustment potentiometer (red rectangle).
Then, as suggested, read off the lettering on the triac and order a replacement. A triac of this ilk should be, say, $1-2. You'll pay more for the shipping unless you find it on eBay and wait a couple weeks for it to come from Asia. Unless someone comes forward with the exact part #, just post whatever lettering you find and one of us will extract the relevant numbers to tell you exactly what to order.
As for the diodes, perhaps someone can identify exactly which diode goes bad. I count about a dozen diodes on the circuit board. It appears there are only 2 types of diodes - 1N4002 and 1N4148. These part numbers are labeled on the board. These a ~5 cent parts. Again, you'll pay more for shipping than for the part and both these parts are on eBay where they are a couple pennies each though you'll need to pony up 99 cents to get a "lifetime" supply since you apparently need only 1.
So to answer you question, I'd say "yes" it's worth your time to take it apart, identify the triac part number, order a replacement, and attempt a DIY repair before giving it to your buddy.
