I'm not sure I correctly understand what's going on here.
Is the issue
- When you request a processor, it starts to insert items into the inscribers, but never actually finishes crafting, or
- When you try to request a second processor while one is already crafting, you can't because your CPU's busy; but if you wait until the first processor finishes, it's fine?
I had assumed #2, hence the wall of text about how, exactly, co-processors and CPUs work. However, if the issue is #1, it means you set something up wrong.
If your setup can't even produce one processor, you're probably putting items into the wrong face of one of your inscribers. The items that go in the top slot of the Inscriber have to be inserted into the actual top face (assuming it's not rotated weirdly); items that go in the bottom slot (i.e. pressed silicon) have to go into the bottom face of the machine; and items to go into the middle face (gold, quartz, diamonds, silicon, and redstone IIRC) can be inserted into any of the other faces.
The tricky part is the fifth Inscriber, which will not work at all unless the three different items are inserted into three different faces, which is not easy to do with only AE. The simplest way to do it is to probably just use Export Buses on the side and bottom to constantly supply it with redstone and pressed silicon, respectively (the silicon one needs a crafting card) and place your Interface on the top, with three recipes: Pressed Gold (I don't remember what the exact name of the item is off the top of my head, but you know what I mean) -> Logic Processor, Pressed Quartz -> Calculation Processor (that's what it's called, right?), and Pressed Diamond -> Whatever the top-tier processor is.
The other Inscribers just need a single Interface on the side, with one recipe corresponding to the press in the Inscriber.
Once you've got all that set up, you should be able to request a Processor just fine. When you do, the network will first drop an ingot/crystal/gem into one of your first three Inscribers, then when it's done, drop the pressed item into the last Inscriber. Since this Inscriber already has the redstone and silicon it needs, it'll go to work immediately.
When it's done, the Import Buses will try to pull another redstone and a pressed silicon from your network. I'm assuming you already have redstone lying around, so the bus on the side of the last inscriber will just take one (if you're crafting redstone somehow, this bus needs a Crafting Card too). The other Inscriber, on the other hand, will need to request a new pressed silicon from your network, so it'll choose a random Crafting CPU to carry that out. This CPU will then drop a silicon item into the appropriate Inscriber, and when it's done, the Import Bus will then transfer it to the fifth Inscriber.