You can't just use cydelete to get rid of it. You need to transfer purchases/backup/restore(preferably as new) then restore from your backup. Then you can rejailbreak. You will need to stay on 4.3.3 or below. So it a bit trickier now that 4.3.4 is out.
Good luck with that but you can check around, layering a JB is going to lead to instability. It works best on a clean slate, if you can even get JBme to work I'll be surprised. It didn't install for me on an upgrade to 4.3.3, I had to restore as new.
Heck the fact that it's crashing on you already suggests some instability.
the only way i see that possible is by running a few terminal commands, but then again, i believe that the .deb has to be installed via iPhone. my suggestion is as chex said, you want to re-jailbreak it. i had this problem a few times in the past and that's really the only way to have a stable jailbreak after something like this. also, why jbme? i used that site a couple of times when first upgrading to IOS4, but since there are a few programs out there that give you a stable jailbreak, why not?
i don't want to assume, but it would depend on how he upgraded. if he upgraded straight from Apple, it could be the jailbreak, meaning it could be that Apple implemented some crash protocol on the jailbreak or the jailbreak itself went bad.
if he got the build from somewhere else, it could be a bad build. it has happened to me a few times.
besides, don't you need a sim to get to jbme anyway? unless, in this case it was an upgrade and/or there might be an AT&T sim. jbme is fine if there's nothing else or one just prefers using the web-based jailbreak.
I think the op had stuff going on with their phone that can't be discussed here... I'm just reading between the lines(shrugs). Thats usually the reason to avoid a restore when your having those problems. Not an issue for the rest of us.