The BarCade was inspired by a number of other, excellent bartops.  Two of them are: Oscar's Happy Hour Bartop MAME and Menace's cabinet.  I began this project with the goal of keeping the expenses very low.  I was able to use an unused PC and monitor, controls I had onhand, and plywood left over from other projects.  Some items still needed to be purchased (a fan, two fan covers, and a handful of other items)  but they totaled less than $40.  The BarCade is powered by a P75 (running Vantage and ArcadeOS over DOS6).

This page shows the progression of the BarCade from start to finish.  You will find the plans to the left.   They should provide some assistance. 

I used an unused 15" monitor that I removed the chassis of and turned on its side.  The tube was masked off and the remaining plastic was spray painted black with several coats.  The blue painter's tape can be seen clearly in the early part of the construction.

For the complete, printable PDF instructions, feel free to download the BarCade document. It includes a wealth of detail to help with your build.

9/22/2013 Update:  William McMahon created two youtube videos (here and here) of his barcade, the "brocade".  The first is the completed project, while the second shows it during construction.  I thought they were very informative and might definitely help future builders.  Thanks to William for sharing.
Here are the basic side dimensions of the cabinet.  All interior widths are 14-5/8".   I began by cutting out the two sides and the base.  The two sides are screwed to the base.   A plywood strip was added near the back to help keep the cabinet square during the construction process.
From the front side.   I cut a strip 4" wide that would be the monitor support.  I measured the monitor to get it centered.   The monitor support is angled back slightly so the monitor face matches the cabinet's angle.
I added a wood support to the rear of the cabinet.  That's the square block at the middle of the picture.   A stop block was added immediately behind the monitor chassis.   From the front.  I added a removable shim to the left side of the monitor to keep it locked in place.  A face was added to the controller area.
Another board was added near the top, immediately behind the monitor's chassis to keep it from tipping back.   A board was cut for the top and screwed into place.   From the front.
The lowly Pentium 75 that would be installed.   All the PC innards removed from the original housing and laid out.  Now the 'fun' began.   The monitor was removed to make the install easier.  The motherboard was the first to be secured.
Next the power supply was secured, using a wood block to raise it a bit and some metal strapping.   The floppy drive got secured next, as it had the shorter of the two cables running to it.   Finally, the hard drive was strapped into place.
The setup was plugged in and tested to ensure nothing was broken during the installation.  Whew!   The monitor was replaced.  Here's a shot from the backside, showing how cramped everything is.   A board for the upper back was cut, with both ends beveled.  An opening was cut in the center for the fan to exhaust through.
The fan was screwed into place.  The fan filter and cover are sitting next to it.   The board was screwed into place.  (I see the screws had yet to be installed for this pic.)   A view from the rear.
I painted the edges of the cabinet and vinyl was applied to the top.    The underside was painted with three coats of paint and left to dry.   The control panel was cut out next.
The simple layout was drilled next.    The joystick area was recessed about 1/4" with a router and straight bit.  The back was painted with three coats.   I drilled out a space for the speaker controls.  A button hole (not shown) was also drilled at the opposite side of the front.
The keyboard hack, which my buddy Steve built for me.   The PC speaker gutted for this project.  The knobs were spray painted black.   This is the sheet of Wilsonart laminate prior to rough cutting.
The laminate for the control panel and one cabinet side is slathered with laminate adhesive (water-based) and left to sit.   Both sides of the cab are covered in laminate and allowed to sit for an hour.   The laminate was trimmed with a laminate router bit.  It cut through the laminate like it was nothing. 
From the backside, I used a 5/8" spade bit to drill a through each button hole.  Then I cleaned up the hole with the laminate bit.   The cabinet is nearing completion in this picture.   A close-up of the wiring mess and the hinge, prior to the control panel top being attached.  Note the white Escape button and the speaker controls.
The final color scheme   The control panel is held down by thumb screw screwed into a receiving T-nut.   The completed BarCade!
Rear profile.   Another shot.   And another.
I'm done now.:-)   Another close-up of the control panel.    

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