Can't set the time

It is possible that your Woods timer is malfunctioning due to a power surge or power outage. You can check the time settings by pressing the "SET" button on the timer and then using the "+" and "-" buttons to set the time. If the timer is still not setting correctly, then it is likely the timer is damaged and needs to be replaced.

It sounds like the timer may have been affected by the power outage and is not functioning properly. If the timer is a mechanical timer, you can try resetting the time on the timer and check if the trippers (ON/OFF pointers) are set to the correct time and are not loose. If the trippers are loose, then they could slip and cause issues with the pump turning on/off at the correct times. You can also try lubricating the manual on/off switch with a lubricant such as WD-40. If the timer is a digital timer, you can try replacing the battery to see if that resolves the issue.

If there was a brief power outage and your light timer is not working, there are a few steps you can take to troubleshoot the issue:

1. Check the timer settings: Make sure that the timer is set correctly and that the time and program settings are accurate. If the timer has lost power, it may have reset and will need to be reprogrammed.
2. Check the power source: Ensure that the timer is receiving power by checking the outlet or circuit breaker that it is plugged into. If the outlet or breaker has tripped, reset it and try again.
3. Check the timer battery: If your timer has a battery backup, check the battery to make sure it is still functional. If the battery has died, replace it with a new one.
4. Reset the timer: If none of the above steps have worked, try resetting the timer to its default settings. Refer to the user manual for instructions on how to reset the timer.

If the above steps do not resolve the issue, it's possible that the timer has been damaged due to the power outage. In this case, you may need to replace the timer or seek the assistance of an electrician to diagnose and repair the problem.

Timer is not identified.
Copy following link to help identify timer
http://waterheatertimer.org/Woods-timers-and-manuals.html

Most modern digital timers have programming back-up that lasts indefinitely in memory until timer is reset.
However current time is sometimes lost with low battery or power outage.
In some timers there is rechargeable battery that protects all settings. This battery is non-replaceable, and can last a few years or more-less.
Since the market is changing rapidly, who knows what remarkable innovation will lessen quality, causing shorter lifespan of product.
Most timers have limited 1 year warranty against defects in workmanship.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Buy another outdoor dawn-dusk timer.
Timers can be damaged by simple power outage, when power resumes there is a surge.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Question posted under Intermatic ST01C, but Timer is not 100% identified since ST01C is battery powered, and should not lose programming or stop working with ordinary power outage.
Most digital timers have a battery or capacitor back-up for power outage.
Add a comment with description of timer buttons, or open link below to see most brands of in-wall timer.

Open following link for to identify Intermatic ST01C and Ei600 and download instructions:
http://waterheatertimer.org/ST01C-program.html#battery
ST01C timer has a battery backup. Power outage will NOT cause battery-powered display to fail, but power outage and power surge can cause any electronic timer to fail.
So either the battery went dead, or power surge ruined timer, or you don't have ST01C timer.

If ST01c display is not showing, then replace battery and then reprogram current time -or- manually re-set timer and then reprogram timer.

1) You performed correct troubleshoot steps down the line.
Last thing would be to install defect timer on another light circuit in house, and see if problem is the timer or wire going to coach lights.
http://waterheatertimer.org/pdf/Intermatic-ej351c.pdf
http://waterheatertimer.org/Intermatic-timers-and-manuals.html

2) EJ351C has 1 year limited warranty.
Buy new EJ351c and install single pole light switch until timer replacement is available.
Timer has easy 2-wire installation. Turn off power. Connect new timer just like old one was connected. Either timer black wire connects to either wire in switch box.
http://www.smarthome.com/25077/Intermatic-EJ351C-24-Hour-Mechanical-In-Wall-Timer/p.aspx
http://www.amazon.com/Intermatic-EJ351C-Programmable-Mechanical-Security/dp/B000Q9YUGU

needs a new control panel

I'm sorry there isn't. Answering machines like this have very little ROM memory. After a powersurge and outage like last night, it wiped the whole memory chip. You can try there support page. It's actually pretty good. http://telephones.att.com/telephones_ui/support/index.cfm