If you're getting a dark grey or purple screen, and the ROMs are good, it's probably a bad connection on the custom chips.
Try running it with no RAM at all - you should get a green screen. If you don't, then the CPU is doing nothing at all. If this is the case, it's probably waiting for the chipset to come back and say it's ok. If the Caps Lock light stops responding after a few presses, then it certainly sounds like the CPU is doing nothing.
If you're certain that the jumpers are set correctly, then there's not much more you can do without a multimeter at least. If you have a multimeter, then check the power rails are within tolerances. The A4000 will boot if the +5V line is more than about 4.7V but if you want it to be reliable you should be aiming for at least 4.9V. The machine will sit and wait until the voltage stabilises at a level it's happy with.
Have you tried just leaving the machine on for an hour or so?
Amigakit know what they're doing, but it's possible a capacitor may have come loose in transit back to you.
Try a different CPU card if you possibly can though, preferably a simple one like the basic '030 one.
Edit: I just re-read your post, and saw you've tried with no RAM. So no CPU then...
Can you please confirm that your 68040 is 40MHz and not the 25MHz? Because if it's 25MHz you want the clock jumpers to be set to INT not EXT...
