UAC not prompting certain users for admin login

I'm the administrator for my company but was not around when the original IT here setup the account settings and whatnot.

The issue I'm having is with the UAC. For most users whenever they try to install a file, add a printer, or make and kind of setting changes, the UAC pops up and prompts for a password. But as I work with more employees I'm noticing that some of their accounts won't give me the option to enter my login and thus, not able to make appropriate changes to their computers.

It doesn't seem to have a real pattern as to who it is affecting (e.g it's happening to newly created users as well as long time employees). I feel it prudent to say that I've got no official training in this field and am self taught. That isn't to say I won't be able to answer followup questions or elaborate on the issue.

Thanks for any help/advice you can give.

Is that happening on an individual machine that many people share (under their own account each) or across many computers for each one? Are they using domain accounts or locally defined users?
A few things to check beforehand would be, that UAC is really enabled where the problem happens and that the users are really standard without admin rights.

Individual Machines. The employees that are affected are able to log into other computers the UAC behaves like it should. They are domain users, I checked their rights/privileges. I checked the UAC settings and it's set to notify normally just like everyone else is.

Of note: Some of the computers are brand new out of the box, others are 2-4 yrs old so I don't think it has something to do with the age/components of the computer.

Ok, it seems to me that it's more related to individual computers instead of users, regardless who is using it.
What happens if you do the opposite? A user whose computer works ok uses one of the faulty ones?
Try also your own user. You should be an admin (I'm assuming you're a domain admin) so you should get an yes/no prompt, while regular users are getting a user/pass one.
Try with different programs, like some control panel applets, notepad, maybe some third party, just to make sure it doesn't make a difference (it shouldn't, but to be sure).

I tested this as you suggested and it is the individual computers. I had one of the users who was having issues log into my PC and they were getting the UAC prompts like they should.

Ok, look at the fine tune options of UAC, maybe the elevations for standard users were disabled.
Do this, run secpol.msc as administrator (you may need to log on with your admin account on the affected machines). Navigate to Local Policies => Security Options and in the other panel for the option "User Account Control: Behavior of the elevation prompt for standard users". This parameter controls what happens when a non-admin runs something as adminstrator. It should be "Request credential on the secure desktop".