Is my phone really rooted?

I am new to rooting and got real excited about rooting my phone and gave it a shot. Yes knowing little I jumped in head first.

First off I used the one-click-method. It appeared to work so I went looking for things to do with my newly rooted phone only to be let down because no other roms really exist for it.(I started to wish I hadn't been dumb and gotten myself in so deep)

Now I install z4root and attempted to unroot.
This app never really worked correctly for me so I was unsure how successful it was.
After installing the root-check app I was notified that my phone was not rooted yet I am unable to get rid of the SupeUser app I got from my original root.I remember reading that im unable to get rid of it because its existence on my phone and purpose for being locked in has to do with my phone really being rooted.
I check the update for superuser and it tells me I need to flash my new binary but after attempting to install it with recovery mode it tells me the zip was not successfully opened. Thus not installed.

Right now I have a fully functioning phone with superuser in place but from what I can tell its not rooted. Can anyone help me understand what the hell I did, and then how to undo it?

Its a droid 3 running 2.3.4

 

I have attempted to run titanium backup and it tells me i dont have root access so its not rooted. Now how do I get rid of the superuser app?

 

Tried oi file manager, the built in file manager, android assistant, folder organizer and if im able to get to the uninstall screen it starts and quickly tells me uninstall unsuccessful. Ive also tried deleting the apk to no avail. I would be happy with turning the apk to a bak but it wont allow me to rename. Any other ideas?

 

I repaired my moto driver on my computer and attempted to root the phone again with the one click method. It recognized the phone unlike it did after my original rooting session and the one click tells me it worked.

what does busybox have to do with this whole thing?

 

Please do tell in detail the file path I would need to follow through the memory to find the apk to change/delete it. I havent been able to see the system/bin path to follow.

 

Root Checker asks for root access and does work in checking root for Droid 3.

 

Update* After the recent update to my droid os this morning I was made aware that I no longer had root access. I used one click again and all was fixed.