Congrats on the kit.

#1. Timer. At first glance, it seems that the relay/circuit in the timer has gone out.
I find it easier to trouble shoot one part at a time. So lets deal with the timer alone. Unplug the color head and plug a regular incandescent lamp into the timer, turn on the lamp, then check the timer to see if it works. Set the timer to something like 10 sec, vs. 00 sec. Only when you have figured out the timer, then plug in the color head to see if they work together.
Did you get a manual for the timer? If not do an internet search for a manual.
Worse case, timers are not expensive. Heck I managed to collect 3 of them w/o trying, like you they came as part of a package.

#1 and 2. That is why I said you need the manual for the color head. Different systems wire the color head/power supply/timer differently. Some come after the timer, some put the timer into the power supply circuit, others .... Do an internet search for the manual for the color head.
Hopefully someone who has a C23+color head can help.

And CLEAN everything. I found that stuff in storeage gets dust everywhere. YUK.