Main Relay Fix
By: Kaspin
(From: http://www.bayareaprelude.com/cgi-bin/ikonboard/ikonboard.cgi?act=Pages;page=3rdMainRelay)

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Problem: Car wont start when its hot out, or takes a long time to start.

If you don't know how to solder or are uncomfortable in repairing your own, you can probably take it an electronics store (not radio shack) and they can do it for you. Or just buy a whole new one.

Part Numbers for new relays:
1988 Prelude 2.0Si - 39400-SF1-003 RELAY ASSY., MAIN (RZ-0045) (MITSUBA)
1989-1991 Prelude 2.0Si, Si - 39400-SF1-013 RELAY ASSY., MAIN (RZ-0081) (4P) (MITSUBA)

What you'll need:
- Philips head screw driver
- Small flat head screw driver
- 10mm socket
- Ratchet with 6" extension
- Soldering iron (I have a 30watt, but a 40w probably would've been better)
- Some solder
- Time. If I had to do it again, I can get it out and back in, in about 30min. But you should probably give yourself about an hour to be safe.

Before starting, be sure you're ready to solder or have a replacement relay ready to go (your car won't run once you remove it).

Remove the coin tray covering the fuse panel.
Remove the 5 philips screws holding the plastic cover under the steering column. (1 in each corner, 1 where the coin tray was)
Unplug the 3 electrical connectors attached to the plastic cover, taking note where each one goes.
Using the 10mm socket and the ratchet with extension, remove the 2 bolts holding the fuse panel up.

Work the panel out from under the dash. You'll have to disconnect some of the shorter wire connectors to get it all the way out.
Unplug the connector from the main relay. Use the small flat head screw driver to press on the tab that locks the main relay onto the fuse panel and slide the relay off.

Remove the plastic cover from the relay. You'll see the printed circuit board and all the solder points. Add a little solder to each making sure you melt the old solder.

Put everything back the way it came out and start it up!

2014 Update from MustardCat:

I recently bought a new Prelude and completed this repair successfully. To add a little more detail to this article this is what I did once I was ready with the soldering iron:

First I used the iron to heat the existing solder. Once it started melting I kept the iron in the puddle for a few extra seconds, so the old solder would turn to liquid and flow around the contacts. I did this for every contact.
Next I melted some new solder onto the tip of the iron so there was a little bit hanging from the tip ready to fall off almost. Then I just lowered that droplet onto the top of each contact point and let it flow around for a second.

That seemed to do it. Some people have reported before that this fix didn't work and I think they might not have been melting the old solder first before adding new stuff.