I have a Intermatic T101-70 timer to control outside lights. It has been working fine for many years (about 15). Recently timer does not turn on at preset time. I have to manually turn it on. But the "OFF" timer is okay. Only the "ON" function is not working. Any reason or suggestion for the cause of the problem? Is it time to replace with new one? Any idea how much a new one costs?

Copy following link to identify timer and download possible manual:
http://waterheatertimer.org/Intermatic-timers-and-manuals.html#HB65R
This timer has 1 year limited warranty from Intermatic.
Timer has photo eye for automatic ON at dusk, and has to be turned away from source of light.

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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

Sounds like the trippers are worn down:
http://waterheatertimer.org/How-to-troubleshoot-Intermatic-timer.html

Buy new trippers and new clock motor and timer will probably last another 11 years.

You probably need new set 156T1978A tripper.
Trippers are made of softer metal and are designed to wear down and be replaced so timer lasts decades.
http://www.grainger.com/Grainger/INTERMATIC-Timer-Tripper-2E054?Pid=search

Open following link for troubleshoot checklist: line 4 applies
http://waterheatertimer.org/How-to-troubleshoot-Intermatic-timer.html

Problem is not clear.
What is turning on-off every 15 minutes? The clock motor? Or the Load controlled by the timer?

If the dial is not rotating and keeping good time, then replace Intermatic T104 240Volt WG1573 clock motor
If the Load is turning on-off every 15 minutes, then that sounds like possible electrical short and not the timer, but more information is needed. Add a comment.

Open following link for troubleshoot checklist:
http://waterheatertimer.org/How-to-troubleshoot-Intermatic-timer.html

Add a comment for more help.

Upvote the help.
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You have two switches controlling same outdoor lights, then that is a 3-way switch
GE timers do not work for 3-way switch.
Aube T1033, Intermatic EJ500, Intermatic ST01C, UPM ETW193 & 350, and Brinks 46-1022 work for 3-way switching.

http://waterheatertimer.org/GE-timers-and-manuals.html#15071
http://waterheatertimer.org/Woods-timers-and-manuals.html#Brinks
http://waterheatertimer.org/UPM-timers-and-manuals.html#ETW
http://waterheatertimer.org/Aube-timers.html
http://waterheatertimer.org/EJ-500-ST01C.html

If you have a battery operated timer like Intermatic ST01C, it may not operate another timer.
The ST01C will not operate circuits farther away than 100 feet, or operate when wires are located underground. Sounds peculiar doesn't it.
I assume these parameters are because of how the battery interacts with electronics inside the timer.
On the other hand, maybe your battery is getting weak.

http://waterheatertimer.org/Intermatic-st01c.pdf
The manual shows incandescent, fluorescent, motors and DC loads.
But manual doesn't specifically include or exclude other electronic devices that might put electronic feedback on the line.

I'll run a test on the ST01C next couple days, and post result on this thread.

I answer questions for free.
I specialize in timers and electrical devices

Below is the manual for the EJ351
http://www.intermatic.com/~/media/files/intermatic/products/instructions/timers/ej351c%20-%20english.ashx
The red light is a good indicator of the EJ351 timer.
The manuals says that you can clear all programming by moving control lever to OFF-CLEAR position for 20 seconds.
After programs are cleared, the red light will turn off.
Then move control lever to ON position, and then red indicator light will start flashing.
So the problem may be that the timer programs were accidentally cleared.
Use the instruction manual to re-program your timer.
Add a comment if you need more assistance, and I will help.

EJ500 has 1 year warranty. The reset button sits naturally lower than other buttons.

The manual shows troubleshooting.
http://waterheatertimer.org/Intermatic-ej500c-manual.pdf

If timer is blank: display bulb burned out; press next/on/off, other timer or switch has turned off power to EJ500.

Maybe a new timer is needed. ST01C (1 year) & EI600 (5 year warranty) each offer same 40-programs per week.

Timers shown above are battery operated, and cannot operate load farther than 100' from timer.

EI500 & GE 15086 offer 7 programs per week ... 7 on events and 7 off events.
http://waterheatertimer.org/Programmable.html#progr

Sounds like the timer may not be getting power.

Turn the circuit breaker that supplies the circuit OFF then ON, as sometimes it's hard to tell if a breaker has tripped by looking at it.

It's possible that the circuit is controlled by a switch that someone may have inadvertently turned OFF.

Also, it's very likely that the circuit is fed from a GFCI receptacle (the kind with the test and reset buttons that are usually found in kitchens and bathrooms) that may have tripped. Those receptacles can sometimes be found in very obscure places. Check outside receptacles too.

If anyone has been digging in the yard or flower beds it's possible that the cable may have been damaged.