OK, The fail point is very early or immediately at power on. While RAM could be the problem I would forget about it for now.
My first suspect would be that there is a short or low resistance somewhere and the 'tick' is the result of the power supply in the monitor shutting down and restarting (what monitor are you using). My second suspect would be a resistance in the power supply line some where.
The first point I would test in this situation is the on board 5 Volt rail. If you have a multi meter then check that the 5 Volt rail is actually 5 Volts. First disconnect the 12 Volt line and Floppy Drive. The 12 Volt line is only used for the floppy. The specification is 5 Volts plus or minus 10 percent (4.5 - 5.5 Volts) however in practice it should be between 4.8 and 5.2 Volts.
Try to test the 5 Volts after the switch. There have been reported problems with the switch after aging. I take the switch connector off the main board and use a jumper block in the socket instead. The ground is easy to find on the board as it is the larger thicker areas that are most common. Most of the smaller chips have 5 Volts on one pin at one end of the chip and ground on one pin at the other end and other side. The circuit diagram will help and look up the pinout of any of the smaller chips. Google the number with 'IC' after the number and select images.
https://www.google.com.au/search?q=7400+ic&source=lnms&tbm=isch&sa=X&ei=TtRbU6C6OM2kkQWX6IDYCg&sqi=2&ved=0CAYQ_AUoAQ&biw=1024&bih=616
https://www.google.com.au/search?q=7400+ic&source=lnms&tbm=isch&sa=X&ei=TtRbU6C6OM2kkQWX6IDYCg&sqi=2&ved=0CAYQ_AUoAQ&biw=1024&bih=616All the smaller IC's starting with 74xx have Vcc and ground like this. Vcc is 5 Volts.
If you don't have a multi meter then plug in the little power light making sure none of the circuit on the back of the little board it is on touches anything conductive or the main board. While listening to the 'tick' sound see if the LED light dims briefly or flashes briefly when you hear the 'tick'. If it dims when you hear the 'tick' then disconnect the main board from the monitor as it may case damage to the PSU power supply in the monitor.
How often (fast) is the tick sound and is it consistent or random?
Test equipment that would help from cheapest upwards -
Digital MultiMeter (ebay $5)Logic Tester (ebay $11)If you have the money then -
DSO (ebay $66)I am NOT recommending the sellers above. The links are just for example pictures.
If you buy a DSO then you don't need the Multimeter of Logic Tester. The DSO I linked to is the bottom of the range and it's usefulness is very limited as a DSO when working on computer board clocked at 4 Mhz. You ideally would want a DSO of 10 Mhz or 20 Ms/s or better. Let me know if you want a DSO and I will look for something suitable. I don't have one unfortunately.
If you get a logic tester then this is the diagnostic path after verifying that you have a stable 5 volt supply.
Test that /RESET on the CPU pin 26 is close to 5 Volts (high and not pulsing). If not replace R101, R111, R145, IC117, IC110 in that order testing as you go so that you don't replace more than needed. or ask for mor detailed info.
Test that you have a constant pulse signal on the CLOCK pin 6 of the CPU. If not test IC117 pin 4. If not pulsing then change IC 117. IC 117 is 74HCU04 and needs to be that so don't use the more common 74HC04.
By 'constant pulse signal' I mean that the 'PULSE' light stays on.
Test that you have a constant pulse signal on the /INT pin of the CPU. If so then CPU and gate array and all associated addressing (glue logic IC's) should be good and most probably the 6845 is ok as well.
Use the working board to compare voltages on CPU /RFESH /M1 /INT /MREQ /NMI /IORQ /BUSRQ, /RESET /READ /WRITE
With a Logic tester they should be -
/RFSH (28) constant pulse.
/M1 (27) constant pulse.
/INT (16) constant pulse.
/MREQ (19) constant pulse.
/NMI (17) permanently high.
/IORQ (20) constant pulse. I should verify this.
/BUSRQ (25) permanently high.
/RESET (26) permanently high.
CLOCK (6) constant pulse. Shown as the slashed 0.
/RD (21) constant pulse.
/WR (22) constant pulse.
/WAIT (24) permanently high.
/BUSRQ (25) permanently high.
/BUSAK (23) permanently high.
/HALT (18) permanently high.
Other places -
Any (only test one per bank) /RAS (pin 4)BANK 1 and BANK 2 constant pulse.
Any (only test one) /CAS (pin 15) BANK 1 constant pulse (CAS0).
Any (only test one) /CAS (pin 15) BANK 2 permanently high (CAS1). I should verify this. Not sure if the refresh uses CAS or RAS.
All DO pins (one per chip pin 2) on BANK 1 constant pulse.
All DI pins (one per chip pin 14) on BANK 1 constant pulse.
All Address pins in BANK 1 (pins 5, 6, 7, 9, 10, 11, 12, 13) constant pulse.
If you have a DI data pin that is not pulsing then that RAM chip or the CPU is faulty.
If you have a DO that is not pulsing then that RAM chip or IC115 or the gate array are faulty.
If you have an address pin that is not pulsing then test two pins on the CPU if it is A0 then test A0 and A8 if it is A6 then test A6 and A14 etc on the CPU. If pulsing on the CPU then several chips could cause this.