Ah, okay. I'm in PAL territory, so your specific use of NTSC in the earlier post threw me.

Is there anything I can do, or am I stuck trying to find a new one?

Either fix or replace.
There's not many caps in the ES10, and I had a guy replace mine for $25 some years ago.

Where would I need to take it to get that done?

I know you're probably not going to be able to give a specific place, but what sort of place would I look for? Normally with these sorts of things I just take it back to the place I bought it, which obviously isn't an option here.

Apparently this is a not uncommon issue with the ES10, to the point where people are offering repair kits.
http://lcdalternatives.com/Panasonic...-P3278862.aspx is a link to but one (scroll down the page a bit).

A web search may turn up something if you are not into DIY electronics repair. There is always the option of a local teenager who is into electronics.

Well, I went to the opposite end of the age spectrum: turns out my dad knows his way around this stuff. Finally managed to get the kit ordered and here and find the time to go see him, replaced all the caps, and it still doesn't power on.

There's a crack running the entire width of the board, which might be the issue.

Next step? Is it possible to get a replacement board, or am I stuck buying another? If the latter, does this one have any value sold for parts?

I'd advise to do what I did on a few occasions in my search for capture gear over the years, which is to take the loss and find a replacement. I must have gone through this three times with VCRs and once with an ES15 that died after only two capture sessions. Would you believe, I once received a VCR with a broken loading door and a tape stuck inside! Another VCR had all of its takeup rollers missing (it was eventually rebuilt at considerable cost anout 8 years ago and still works today, 25 years after it was made). So this is a dubious welcome to a club that is far from exclusive for many members here and elsewhere. In my case I took the required action(s) right away.

A cracked board is obviously not working, any more than it would work in a PC -- yes, I had one of those, too, not a cracked board but a completely dead power circuit that refused to respond to replacement power supplies. Since then I've built my own PCs (and encountered one brand-new but defective power supply along the way) , but that's not much of an option with DVD recorders.

If only I'd plugged it in when I first received it...I got three or four machines on the same day and the ES10 slipped by me. There's no way it was in working condition when it was sold.

Unfortunately I've already spent more than I can really afford.