Clicks like starter problem but pop the clutch enough and it starts

I have a 2006 Mustang Stage 1 Rough and it's giving me problems. I go to start it and it makes the clicking sound, already replaced the battery. If I pop the clutch enough times, it starts. Also when shifting from 1 to 2 it is sluggish and hesitates. I am woman btw so my lingo may me out of context. One person thought it was a lifter but it's fine, it does tick but every mustang I have owned does that. I drive the out of it. It's now sitting because my husband doesn't want to pay for a tranny and clutch. Please help. I miss driving my Harvey, yes that's his name

Yes, Harvey has the original clutch with 56k miles. My brother checked the lifters, the old fashion way with a long screwdriver? He's old school mechanic. This new stuff all digital makes him crazy. Thanks for the tip on cables.