I agree, it would be easier to just use the existing board instead of pc.
Where you planning on using the pc monitor? The original arcade was a 19" standard arcade monitor.
Since either route requires a cabinet, controls, wiring, I assume those constant as that is not where the price differnece will be. And I am going to assume build a new cabinet with new parts.
If you need to get a monitor, as this would be the most expensive part, a used but in good condition 19" standard monitor is not that bad, considering it is the most popular sizr monitor for arcades.
Then you'd just need to get a standard arcade power supply, those are like $14.
Then some speakers, again, cheap.
Then it is a matter of wiring everything to jamma (and getting a jamma harness from bob roberts).
You also have to realize that double dragon isn't really worth anything these days. you could probably pick one up somewhere for $200, then have it shipped.
I think I am a rare example BUT I have a Double Dragon II cabinet (with Double Dragon I and II boards). I got it for free. When I was looking around for a cabinet to put a pc in I came across a local vendor and he had cabinets in his warehouse that he would be glad someone take off his hands so he'd have more room. Out of the lot I picked the best looking cabinet. It happened to be a fully working Double Dragon II is decent enough condition, just no monitor. I decided to build a cabinet instead afterwords and I plan on refurbishing the cabinet (as I stole some parts form it for the other cabinet). Unfortunately due to events like unemployment I just haven't been able to buy a monitor for it.
However, you probably could make a double dragon cabinet with used parts. Just find an empty jamma cabinet locally, with monitor preferably. Without monitor I'd say pay no more than $20 unless it is in mint mint mint condition. But any generic jamma cabinet will do. A jamma cabinet is just a cabinet that is prewired with a jamma harness (and probably a standard power supply and speakers) so all you need to do is add the game board. Hopefully you can get one with 2 player, 3 buttons each player. Otherwise you will have to modify the control panel.
If it doesn't come with a monitor you can probably find a decent used standard arcade monitor for under $80, sometimes in the $50 range.
You can get a Double Dragon I (and II) board off ebay for $5-$10.
The only way you can legally emulate Double Dragon is if you dumped the roms yourself from a board you own, and keep the board.