I'm guessing your weird cap (with no picture) is probably a polyester cap, shaped like a pillow, probably brown or blue? These guys rarely fail so probably doesn't need replacing. You can ask Mr Google "capacitor types" and get some answers.
FWIW, IMO cap-kitting is largely a waste of time. For most TVs and monitors over 10 years old, most or all of the caps will still be good unless it has been worked hard. Even then they will mostly be in the power supply sections. Failed caps will often be obvious on inspection. If not, failing caps will show up with an ESR meter like the blue one from Anatek or the old Dick Smith original. ESR meter allows you to check basic electrolytic cap health without removing it from the PCB, saving you time and money and saving your PCB from unnecessary wear and tear from needlessly removing/replacing caps. Even experienced solderers can occasionally screw up a solder pad or something else by accident, it probably isn't worth the risk for inexperienced people.
I know some of the arcade parts/supplies retailers love selling cap kits, and that's fine and good, but maybe more of them should try selling ESR meters as well.