@jdryyz
OK, I hadn't looked at the posted link in detail (I only saw the A3640 jumper settings). Well, at least I got'em right! :-)
Unfortunately then it sounds like either an incompatibility or a dead A3640.
Here are a couple more things to try:
1) Put up the brightness of your CRT so that it's not black but grayish. Turn on the Ami and note if the color changes to an even lighter gray. If so, the CPU is good. Otherwise, replace the CPU and try again.
2) Assuming in the above test the CPU is good, put your nose very close to the SMD capacitors (5 of them IIRC), and smell them. If there is some nasty stench, they've leaked. Also check to see if their solder pads are fuzzy vs. shiny. If shiny, no leaks. If fuzzy, they've leaked.
3) Desolder and replace the crystal oscillator. It could be dead. Unusual, but it's a possibility. In fact, before you desolder the crystal oscillator, I'd personally get some el-cheapo electrolytic caps and replace the SMD ones. You'll need 22uF @ 16Volts. Here's more info you'll need, because they've been soldered on backwards:
http://amiga.serveftp.net/A3640_capacitor.htmlGood luck!