Unbolt the caliper and move the piston in and out, without disconnecting from brake line. If still not operating freely, then rebuild. I would buy two rear brake cylinders and replce them if needed. They usually rust up when a mini sits for a long time.

Well, it's running. I thought it had been 2 years since it ran, but I looked at my mileage log today when I drove it to the gas station. I've only driven the Mini 50 miles in the past 5 years. She ran pretty well in the 4 miles from here to the gas station and back.

Items that still need attention: - Add fuel filter before carb to catch any crud that might come up from the fuel tank and lines - clean brakes and change brake fluid (I think the left front caliper is sticking a bit) - Get fuel and temperature gauges working - front end alignment

A huge thanks to Brad (WillieB) for helping me clean and adjust the carburetor.

I drained the tank and added brand new fuel. Whatever may have been in the lines has been used up by now.

Did you drain out all of the old, stale fuel and replace it with nice fresh fuel? Fuel goes stale pretty quickly these days.

Yes. The vacuum tube is connected and seems to be flowing properly. Spraying carb cleaner at the joints doesn't have any effect so assume it's not leaking.

Do you have vacuum advance hooked up to the dist? Check the fittings and hose.

Unfortunately HIF carbs require more effort to clean.  If the float bowl cover/base has not been removed in a long time you may want to order a rebuild kit as the seal is likely to be hardened and may not seal again when you refit the cover.  I believe some HIF carbs have a screen filter right before (or built onto) the float valve.  That is another place that gum, varnish, and debris can build up and block fuel flow.   Regardless, make sure the ignition system and components are in good order and adjusted properly before working on the carb and mixture.

I neglected to respond to your comment about brake fluid.  I think it is a general rule of thumb (even with modern cars) to replace the fluid every 3 years or so to remove moisture from the system.  At one time Castrol DOT-4 was labeled "LMA" which I believe was for Low Moisture Activity (or Absorbtion)... but I think even it was supposed to be replaced every 3 or so years.  

Thanks Doug. It's an HIF 44 carb. I'll take care of the items you mentioned.

Your post implies the car sat for a while.  Though you have gone through carb adjustments, you probably need to clean the jet, needle, and connector tube between the float bowl and jet (assuming it's an HS series SU).  After that you will need to adjust the carb again.  However, put that off until after you have given the car a complete ignition tune up and valve adjustement.  When working with the carb also replace any fuel filters and make sure you check and adjust the float valve setting.

I worked on my cars for the first time in ages yesterday. Last week, my son and I got the Mini to start and idle reliably for the first time in over a year. The carb adjustment was way off. Played with it a bit more yesterday, topped off the dashpot oil, flushed and refilled the cooling system and richened the fuel mix a little more and I finally took her down the street. She's running like crap, but she's running. She starts pretty quickly and idles well, but when I give it some gas, it bogs down and occasionally backfires. Any ideas? Also, she's been sitting for almost 2 years. Should I replace the brake fluid? It's DOT4 and it was pretty fresh when I stopped driving the car. I've heard that some brake fluid absorbs water from the atmosphere over time. Aside from getting her running, the next job is to replace the seal where the shift rod enters the transmission (I hope that's the source of my oil leak). Sounds like a pretty simple job; is it?

Somewhat OT: I did my first valve adjustment yesterday on my 1987 BMW E30. Much easier than I expected. It's running much more smoothly and the valve noise is gone. Hopefully, the new valve cover gasket will take care of the pesky little oil leak that's been bugging me. Still can't get the darn brake light warning light to go off. All the lights work; I've replaced the bulbs with the recommended nickel base bulbs and I replaced the switch yesterday.