Alright let me give you a run down in bullets just so it's easier

-Our rythm guitarist can't play
- He brings all three of us down because of lack of skill
- Just bought $600 worth of new equipment such as new guitars and pedals
- But he can't play though, he sucks he can't even do simple chords
- We had our first show and his playing was horrid, my drummer who had the mixing board turned him down so it wasn't noticeable.
- If we kick him out he will probably cry, he is sensitive as a mother****er.

I mean what should we do?
Why did you take him in your band in the first place?
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"Maybe one day we'll wake up and this will all just be a dream"
Teach him how to play or make him fight someone else to stay in the band. No weapons, though. That would be mean.
my band had a very similar problem a few months ago, with our rhythm guitarist too, except he could string a few chords together well enough to play with us. but he was a very lazy person, and as the rest of us progressed quickly, it seemed like he never learnt a single new thing. and like yours, he was a over-sensitive person.

but we all knew that for the good of the band, he had to go, the last thing you need is someone holding you back. just let him down lightly and tell him you don't think he is the roght guy for the band at this current time, but you could always jam together(you're not actually gonna do this, it's just to keep him sweet) and stay in contact for future references.

make sure everyone else in the band is on the same page as you and wishes to kick him, and you'll do fine, because you have the majority. some good advice though, no matter how bad he moans and tries to get symphony from you, don't let him stay, it will only make matters worse down the line.
I've got the same problem. A Vocalist with a mother that would eat babies in her rage. And hes hormonal like you wouldn't beleive. We played a live show and everyone said we we're great, except for the vocals. Even the sound guy at the gig, who didnt even know us, turned him down because he's so horrible.
Tell him to be glad he has the opportunity to play in a band... it's a privilege. If it doesn't motivate him to practice like sh*t and improve, than he deserves to get kicked out. I'm playin with a band of guys WAY better than me right now, working 60 hours a week and practise all night every night to be sure I nail everything and properly support our lead guitarist. Sounds to me like he's into the idea of a band... but not the hard work that goes into one.
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The deadbeatS

Do What Your Love Tells You
haha my rhythm sucks ass to, im guessing he's only in cause he's your mate?
mine bought some gay pedal instead of a bigger amp, when i called him retarded he looked like he was gonna have a little bitch attack and start crying..... i say give teaching him a shot, and if that dosent work, kick him out.
Honestly, I would tell him that he needs to improve. If you tell him to work harder, and he doesn't, then I would kick him out.
I don't know why you've kept him in so long if he's so bad, you really shouldn't have. I'll guess that during this entire time you haven't mentioned it to him either. You really should, now. Tell him what he's doing wrong, and to try to fix it. Wait, and if he doesn't get better, then kick him out.
And no, Guitar Hero will not help. Even on expert. Really.