Fix semi working PCI backplane

I have designed a 2 slot PCI backplane to host a computer and an ADC card. The board is 2 layer (top and bottom), all the PCI signal lines are on top, bottom is almost entirely ground. The board works with the computer I'm planning to use (Advantech PCI-7031N) and the ADC card, along with several other PCI cards I had lying around (ethernet cards, modem cards, USB cards). However it does not work with a much older Advantech computer (PCI-6771) which leads me to believe the signal integrity is not within PCI specs. This is consistent with the fact that I have zero experience with high speed signal routing, basically I have looked at the PCI specs, understood which signals go where, routed the signals using "shortest path" philosophy and hoped for the best. I can provide CadSoft Eagle .sch + .brd files, populated board (the one on the pictures), and the computer (if necessary). Your job is to fix the PCI signal routing and make it PCI compliant (5V signalling) so that the backplane works with any computer and PCI expansion card. Measurements (or some other form of assurance) are required. If 2 layer board is absolutely a no go, 4 layers are possible, however I would like to avoid that as much as possible due to much higher manufacturing costs.