Sound like you shorted something out.
Look closely for solder blobs, dirt or components that might have gotten bridged with some solder.
Main goal is to try to figure out whether your power rails are still working.
If you don't get the expected power after pressing the power button, maybe you blew something in the power circuit.
(Note that the Switch will not boot into OFW without a battery).
There is a ton of information on the following website for an original Switch but the OLED uses the same components.
Some pages have information about measurements without connecting it to a 1v power source.
Maybe try those first in case you don't have a lab power supply.
Since it is already broken, you might as well plug in the power cord.
Another quick MacGuyver test is to dip the components of the power circuit (MT92/P13USB) with some isopropyl alcohol to see if something gets hot and evaporates the alcohol more quickly than other places.
It does only give an indication because the root cause might be somewhere else.
https://www.retrosix.wiki/33v-regulator-checks
https://www.retrosix.wiki/first-stage-boot-short-checks
https://www.retrosix.wiki/full-boot-from-bench-power
This page also contains a lot of details in case something around the MT92 has gone bad :
https://www.tronicsfixforum.com/t/n...ents-showing-weird-values-all-around/11416/15
All component values around the MT92.
https://www.ifixit.com/Answers/View/675722/What+is+this+component+next+to+the+M92T36
And if all fails, just reach out to one of the repair guys/girls on the forum here.
In most cases, your Switch can probably be fixed.