Slacker, why do you use the regular expressions when it has nothing to do with the commands? If the regex is used, you should change your code to this:

on $*:Text:/^!(kickme|kickbanme|banme)$/S:#:{
  if ($regml(1) == kickme) { kick # $nick Kicked on request }
  elseif ($regml(1) == kickbanme) { ban -ku30 # $nick 2 Kick + 30 second ban by request }
  elseif ($regml(1) == banme) { ban -u30 # $nick 2 | msg # $nick activated a 30 second ban by request. }
}

Otherwise, you could just use:

on *:Text:*:#:{
if ($1 == !kickme) { kick # $nick Kicked on request }
  elseif ($1 == !kickbanme) { ban -ku30 # $nick 2 Kick + 30 second ban by request }
  elseif ($1 == !banme) { ban -u30 # $nick 2 | msg # $nick activated a 30 second ban by request. }
}

you could put them under one event

on $*:Text:/^!(kickme|kickbanme|banme)$/S:#:{ 
  if ($1 == !kickme) { kick # $nick Kicked on request }
  elseif ($1 == !kickbanme) { ban -ku30 # $nick 2 Kick + 30 second ban by request }
  elseif ($1 == !banme) { ban -u30 # $nick 2 | msg # $nick activated a 30 second ban by request. }
}

My apologies, I forgot the $chan.

on *:text:!kickbanme:#: { !ban -ku30 # $nick Kick + 30 second ban by request }

You only need $chan or # when it's an event. For aliases, however, $chan or # are not necessary.

I just used that as a test on my bot, and it didn't do anything. But when I typed /!ban MyNick on the bot, it did. Which is weird.

The status window showed this.

• /ban: invalid parameters

Sounds okay. :-)

You can also use the power of the prefixes that mIRC's default /ban has, to kick+ban the user.

On *:Text:!kickbanme:#: {
  /kick $chan $nick Kick + 30 second ban by request
  mode $chan +b $nick
  .timer 1 30 mode $chan -b $nick
}

can be also rewritten as
on *:text:!kickbanme:#: { !ban -ku30 # $nick Kick + 30 second ban by request }The -k switch means to 'kick', and the u30 switch means to (unban or unset, either one works) in N seconds. The 2 after the $nick is the ban mask. The kind of ban mask you supplied wasn't a real one as it was a nick ban. I prefer using mask 2 as it is the most "unique" ban mask out of all of them.
In this situation where you're "playing around", almost any ban mask is fine, unless you share a channel with a few dozen New Yorkers with the same ISP. You can use the same concept that I used, but with the "ban me".

If you noticed, I put

/!ban

instead of

/ban

.
Using ! before a command means taking the original one (very useful when dealing with common mIRC default aliases such as /kick and /ban). This means it won't take any modified aliases that a person who might use this script has; it's safer this way, and can prevent errors.