The batteries are integral to the NVRAM chip and cannot be replaced without the careful use of a Dremel etc.
Some NVRAM chips can still be bought new on Digikey and Mouser, but the Watchdog/Timekeeper one with the RTC inside is completely obsolete, hence my suggestion of the reproductions from ebay.
If you are handy with a mill (or really steady with a Dremel), you can machine off the top and expose the coin cells to solder in new ones, you can find xrays and pictures and guides around the net on this process.
You can still talk via GPIB if it doesn't boot. I would suggest trying to read out the NVRAM data as soon as possible, if you get a good read, it will make your life easier.
https://www.eevblog.com/forum/repair/unified-tektool-released-!-(firmware-flash-tools-for-old-tds-series)/msg3758918/#msg3758918Also, check your error log, see if it says anything there.
Also also, do check the SMD capacitors on the acquisition and main boards (bottom and top respectively) for leakage, I'd replace them regardless as its a very well known issue.
And also while you have it apart, check the PSU board for Rifa caps (4x 1000pf or 2200pf 10mm pitch caps IIRC) and replace, and check for the presence of capacitor C17 (47uF, 80V LOW-ESR electrolytic, feel free to increase voltage rating a bit) roughly around the center of the board if your board revision has it, replace it immediately too. It's for standby power and if it goes high-ESR, it takes out some TVS diodes and a transistor that kills your standby power so the scope won't turn on. As it is in use whenever the scope is plugged in even when turned off at the front panel, it's old now, it does need replacement...