Yeah, I replaced my chip with one from China, and I'm pretty sure it arrived in under a week. And at $2.50... it's hard to go wrong...

 

Ah, so apparently the removal of the capacitor could also be causing the problem that I'm having. So I'm going to try replacing the capacitor first and see if that works out. If not, I'll be ordering the chip from China.

 

uh, yeah. capacitors are generally real important to the circuits they are in. you need the right capacitance (uf or ufd, really µf == microfarads), and the same or higher voltage and temperature spec as the original cap. don't go too high voltage, or it might be too big to fit. I get mine from DigiKey Electronics - Electronic Components Distributor, they have *EVERYTHING* electronic, their catalog can be overwealming. search for aluminum electrolytics, if both leads were out the same end of a cylindrical, thats called 'radial' (1 lead out of each end is 'axial'). get japanese NOT chinese caps. rubycon, nichicon, panasonic are good brands.

if you had leaky caps, clean the board really well with a small brush and a can of circuit/contact cleaner (NOT motor cleaner). like spray the board down throughly wherever the capacitor spooge went, brush it while its wet, spray more, brush more. I use a 1/4" wide cheap art paintbrush with its bristles cut to half length so its stiffer. if any of the capacitor flug got under the chips leads, wash under there real good, and poke at it with the brush as much as you can, while flushing it with cleaner. avoid getting the cleaner inside any motors or whatever.

 

Awesome! Replaced the capacitor today, and the odometer works perfect. Speedo is a little bouncy, but that might just be because I'm running the car on jack stands.

Thanks pierce and others who helped!