[Jeffhs]

It might. Any bad capacitors in that set (or any other) will cause problems of some sort. I'd replace that bulging cap ASAP, as it is of course defective. Once it is replaced, your set may well work like new again.

I'd also look for any other caps that have bulges (especially on top) or other signs of defects. Any time a capacitor bulges and the bulge is noticeable (even if it isn't), it means the part may eventually explode and cause other problems; in any case, the cap is definitely defective and must be replaced.

I imagine (don't know for sure) that even tiny electrolytic capacitors such as are used in today's electronics (not just televisions) can explode violently if they are overloaded to the point of the casing being distorted, and if the device in which they are used is not shut off promptly. What is probably happening is that the capacitor is getting so hot the electrolyte solution inside is literally boiling and producing steam. The small capacitor cannot take the expansion caused by the steaming (there is no outlet for the steam in these components, so there may be no smoke or other telltale signs of trouble), so it can or could explode -- not unlike standard tubular electrolytics in tube-type radios and TVs when they short or otherwise become defective.