EPSON ET-2760, suddenly no power after printhead deep clean.

How much cleaning fluid did you use when you did the manual clean? Generally, unless the printer has been sitting for years at a time (or you found it in a thrift store, which is almost certainly a surefire way to know you have a horrible clog that will be harder to clear), you usually do not need to use a lot of cleaning fluid -- just a few mL of the liquid. I suspect the fluid got onto the motherboard or power supply, as the power supply on many of these Epsons is sealed but not completely protected from ink/liquid penetration.

It's been a good minute since I had an Epson printer, but their newer units (2010+) have a screw on the back for the power supply you remove. You can dislodge the power supply -- however, this is based on the cart units, which are a little different than the modern "ET-" printers compared to the early units we had in the US, which were hacked together with the ink chip monitor deleted (and likely programmed to 100% permanently). These also have a line-in box for the fax module, which may cause the same problem if it gets damaged (even if you do not use it).

I would first see if the power supply is clear -- if it is, it's probably fine, but you may want to mentally prepare to potentially have to replace it as it's in the line of fire of the ink path on most Epsons. Depending on the hardening of these newer Epsons (which, compared to the old days, is a lot more hardened due to the modern ink DRM; it's hopefully removed with "ET-" firmware but Epson might just permanently set the ink levels to 100% like the early units or they disabled the stop print "feature"), you can potentially disconnect and delete the fax module if you do not use it and that fixes it; however, the hardened firmware may throw a fit.

The reason I know about this is it used to be doable on a LOT of older printers (or the printer ignored it when it broke down like the pre-DS HPs) and if you got a deal on a unit with a good PC but a dead fax, disabling it or removing it was fair game (note: this predates HP DS) and very often, you scored an enterprise-grade printer for nothing but your time. These days, the only way left to do it may be to disable it in firmware (as I did on my MC3326 to shut the unit up and silence the alert LED since I don't use the fax and a lot of AIO lasers seem to have it) and leave it inside the printer.

If the power supply is fine but a damaged fax card is causing problems, try to run the printer without it connected if it operates without it. If it works, remove it from the printer to avoid confusion (and put a label over the RJ-11 ports!).