DO NOT TAKE OFF TEHPLYWOOD ON THE BACK WITHOUT BRACING THE STAND>
If you remove the plywood on the back, the stand will lose shear support and teh stand could just lean over and collapse.
Put a cross brace on teh front then take theplywood / particle board off, then install some 3-5 ply wood.
As for the front, it is basic carpentry to make a face frame out of whatever wood you wish for your finish, (i.e. 1x? rim wood, liek 1x3 on teh ends and 1x6 on the top and maybe one by 8 on teh bottom. USe dowels or biscuits to glue and screw the pieces together, witht eh side pieces resting on top of the 1x8 ont eh bottom, and teh top piece on top ofhte 1x3s,.
Once the screws and glue has set, you will have an opening, that will frame the doors. The easiet type of doors will be 1x3 trim, that has one edge of the board has a notch cut into it, then install some 1/8" vaneer ply in that notch, and but joint the four pieces to make the door frame.
Teh doors should overlap the face frame by one half inch on three sides and hopefully comewithin a1/16" at teh joint between the two doors.
If I had a picture of this process it would be much clearer, and rather easy if you have a table saw, some long clamps fo rthe doors and the face frame.
Trying to straighten or install doors onthe 2x framing members you have will be hard and not come out too well.
Good luck, and hopefully someone can show you some pics.
Bill