I think it makes more sense at this point to bid a fond farewell to the old monitor if it is ADC.
The problem is that Apple's ADC monitors ran power, video and USB through one cable. It's the "power" side of the equation that requires the brick; the monitor can't get power from the wall like a regular one does. The Apple genius was wrong. Those people seem good with current gear, but are commonly weak on older equipment made before they had to use underarm deodorant daily.
Original Apple adaptors are sky-high in price:
I recall there being third-party adapter like Dr Bott but they are also discontinued and scarce. I looked for one about two years ago and they were already around US$100.
For $100 you can get a nice flat-panel monitor and, for $150 you can get a really nice FP monitor.
I am an advocate for keeping old technology in service and out of the landfill, but ADC has to be scored as an Apple failure in the long run.
EDIT: Forgot your monitor was probably newer than the pre-1998 equipment this forum served. You may want to look through this part of the forums where older displays are discussed:
to see it there are any better workabouts.iMac 27-in; Mid 2010 2.93G i7 Quad, Mac OS X (10.6.8), 4GB RAM; ATI5750 1G VRAM
"I'm told by a genius at our local Apple store that I need an ADC to DVI adapter."
When describing an interface adapter, it's important to get the terminology correct - or you could end up with one that doesn't suit your need. You're converting the computer's interface for use with the peripheral, rather than the peripheral's interface for use with the computer, so you need a "DVI-to-ADC" adapter. The ADC-to-DVI adapter enables connection of a modern DVI display to an older Apple computer's ADC-ported graphics card. In your case, you need the Apple DVI-to-ADC Adapter (Model A1006), which retailed for $100 when available. If you check eBay, you can find many listed, such as this one. Most of the sellers are trying to get what they paid for it when new, so scarcity is what maintains its value. As Allan mentioned, you can find new LCD or LED disdplays for not much more than that adapter sells for. In spite of that, there are still many of us in the Forums, who invested in hardware upgrades or adapters that exceeded the value of the older computer or peripheral that we wanted to use.