IBM Z60T randomly turns off, both on battery and AC power. Have checked the power settings and are set at default, have tried other settings as well

Reset BIOS to default settings. Perform Flee Power - remove the battery and any other peripheral device connected to the computer. Hold the power button for 10-15 seconds and then connect only the AC Adapter and turn ON the computer.
If none of the above said helped to resolve your concern, I strongly recommend you to contact our technical support for assistance.

you will have to re install your opperation system

Just after that there was NO correct answer to fix this problem causes the problem not solved even if it is marked as solved. Me too I have this problem, I was fix it by setting jumpers to default 60 Hz AC power because I won`t have 50Hz AC power or some AC power converter before PSU, I mean this is voltage errors, it`s need to be set to default +5V(60Hz) PSU not +5VSB(50Hz) PSU, (Step1) like might be set to USBPW12 to pin 3 both USB to right side inserted jumper it`s in left side of, near ATX 12v advanced CPU power cable connection socket. Next (step 2) is set up front USB jumpers to +5V or system won`t start up, it`s on motherboard about between PCI1 and PCI2 on right side it must be set to USBPW56 and don`t set it to USBPW78(5+VBS) because system won`t start up, the jumper must be set to right side I mean it`s last jumpers to right side need to be set up, because it`s +5V(60Hz) PSU supply. The USB wake-up feature requires a power supply that can provide at least 500mA on the +5VSB lead when these jumpers are set to +5VSB otherwise the system won`t power up. Next step if it still not starts up its BIOS fault, it`s easy to repair, just (Step3) turn off PC remove BIOS battery (it`s down to IDE cables), start it up wait a bit, then turn it off and turn it again on wait a bit again, turn it off place BIOS battery in to socket to be able save BIOS settings i mean battery is need to save them otherwise settings won`t be saved and Chassis will be broken. (Step 4) Turn PC on press del key after BIOS is load in open Power\Hardware monitoring\Chassis Intruder set to Disable, save settings exit. (Step5) If BIOS (PC won`t power up) it`s Chassis1 jumper fault, it`s need set to Default (Chassis signal, and GND(Ground)), it`s between SATA 2 and SATA1(Serial ATA connectors 7-pin it`s near and down to BIOS battery, the jumpers might be set to right side, after it`s completed repeat Step3 and Step4. CMOS is BIOS battery. If that all doesn't works Take BIOS clearing jumper in it`s clear state, near BIOS chip. Turn on PC with CMOS clear jumper turned on its work. Take beck jumper in its default state after that take bios chip out and CMOS battery out both them an two times restart PC after insert all beck if PC will be working all keyboard flashes once, after its in AC power.

Motherboard repair

BIOS Battery

Chassis repair

your laptop power supply is not working properly.so you can checked it from laptop service center.

did the monitor turn off when it is in idle mode? it might be the monitor power options (it might have been set that when it is idle for an X minutes it will turn off). check the monitor power settings.

Sounds like a bad battery to me. If you have a DC voltmeter you can check the battery.

This could be a couple of things. Start by checking the power supply with an ohm meter for the proper output. 1 volt over or under will need a supply replacement. The system could have glitched by being ran with a bad battery. Go to IBM's support site, download the bios or any updated bios version, and flash the bios. If this doesn't correct the problem, then it's going to be a failure with the power management system on the motherboard. You can take it in for a diagnostics to find the exact problem area, but most likely they will tell you motherboard replacement. Motherboard replacement is generally the only option with a failed power management system

When starting laptop on first screen hit "Delete" or "F2" (not sure which one on thinkpads) go into the setup and check the power settings restore to default and save.

First, you should clean the battery terminals. You can scratch the terminals with a metal and then charge. Secondly, you should change your battery, that is, buy a new battery.

When you turn your laptop on press F2 to go to the system settings Continue to press alt+p till you get to a page about battery usage then turn everything up to max. hope this helps