I would suspect the cap. If you have an old fashioned analog meter, like a Simpson 260, you can get an idea of its condition. Before you remove the cap connections for testing, be sure to disconnect the incoming power, etc to make this a safe endeavor. You also should discharge the cap. The proper way to do this is to clip a resistor (I use a 1k 2 watt) across it to bleed it off safely. Most people just jam a screwdriver across the terminals. It may spark so if you do that, don't use your favorite SnapOn for this. If it doesn't spark, that's the first sign that it may be bad. Using your meter, set it to read in the 10k range and measure the resistance of the cap. It should start off with a low ohm reading, then as the current passing through it from the meter, the resistance changes and should go high. Higher the better. As caps charge, they become something of an insulator, very loosely speaking. If it measures open, or very high ohms (true open is infinity, no reading, no meter movement), then it is bad. If it reads low, just a few ohms, and stays low, not charging, it is likely bad.
On the other hand, some of the newer DMM's have a cap tester built in. Or, some supply houses have cap testers and can test it and sell you a replacement. Your case does sound like a bad cap to me. The DMM cap testers are not the same as the old style bench cap testers that actually used the voltage the cap is rated for. That is more of a real world test and is, IMO much more reliable. But they are better than no test at all. Of course, since you have noticed a bulge, it it probable that you have a problem, so you will either go to a supply house where they can confirm it, or find a way to test it yourself, even if only with a analog meter, and buy online.
