Depends on the Laptop
This really depends on the laptop. If it just needs a stable DC supply, that can be done, but if it requires an activation signal as a brand-lock-in annoyance, then you are in for a lot more difficulty!
How you would produce a moderately high current regulated DC supply would depend a bit on era. In the solid state one, semiconductor diode regulators and transistorized regulation yields a fairly straightforward and practical design, albeit with a much heavier power transformer than the tiny high frequency ones used in today's switching supplies. Probably you can find something suitable for borrowing in an existing product (though perhaps not a consumer one). In an earlier era you may need more complicated rectification schemes, and high power low voltage filter capacitance will have to come from a very large array of low value capacitors. You may well end up with an AC operated motor driving a DC generator.
Lead Acid Cells
Another option to consider would be storage batteries. For example, one and a half "12v" car batteries starts to put you into the right range, and you are mostly targeting an era when car batteries would have been a maintainable array of individual cells held in a common crate, so getting a series connection of nine of them (one full battery, and 3 of the 6 cells in another) should not be hard. You can either charge the battery before use, or possibly use it as a bit of a stabilizer/regulator while connected to a power source.
Emulate the Battery Pack
If you do have a laptop which requires a brand-specific activation signal from the power supply, an option might be to disassemble the battery pack and try to emulate that, probably with some different number of contemporary chemistry battery cells, rather than provide the DC input. You may need to put some thought into emulating the output of a thermistor or other sensors. If the battery has an on-board management IC, you'll have to hope you can somehow generate conditions that satisfy it. Presumably you will shut the laptop down and charge your replacement battery independently of it.
The USB Tragedy
Once powered your computer will be usable as a manually interfaced data processing machine. A relay team of typists could accept input and produce output, but this will limit utilization of this unique-in-the-world resource. Back in the day when hardware serial and parallel ports were present, building an interface widgit with vacuum tube technology to collect inputs from and channel output to dozens of proto-teletypes would have been possible, but with the "legacy-free" switch to USB, not really. About the best that could be done if you decide to donate your services to a larger organization would be some kind of electro-mechanical speed typer to submit input jobs, and perhaps a film camera for capturing output ones for distribution back to the submitters.
It may be a good idea to remove the lower case of the laptop and build it into a console providing more and better filtered cooling air than the tiny ordinary fan can. If the keyboard fails constructing a replacement is actually fairly possible (which gives another input idea, but one whose risk may not be justified before the need). If the hard drive goes, you are in for a lot more trouble. With a PATA interface and the lucky accident of having brought printed documentation you might get somewhere towards constructing a replacement with 1970's digital logic or 1960's research-lab capabilities, with SATA you are out of luck, unless you want to have a go at emulating the bios flash.
While it will be painstaking, while the machine works you'll probably want to do a hex dump of the bios, boot sector, etc and photograph every page for preservation.
Better an older laptop
For many of the reasons threaded trough this, you'll be best off with a laptop from the 1990's or even the 1980's. It won't be as absolutely powerful as a modern one, but still many orders of magnitude beyond any contemporary alternative in your destination time. More importantly, it will be more maintainable and interfaceable. The battery pack will be built around simpler NiCd or NiMH cells, the power input won't require an activation signal, the disk interface will be one old technologies could emulate and there will be I/O ports within the realm of interfacing, etc.