No, uninstalling and re-installing will not change the permissions at all, so your problems will not go away when doing that. Coppermine is not a desktop app that you uninstall and re-install to make issues go away, so that's generally not a bright idea.
Why don't you do as I suggested and review the permissions section of the docs instead. It's important that you understand permissions - you will need that piece of knowledge not only for coppermine, but for all sorts of pre-made scripts. It's important that you
understand how permissions work. As suggested in the
permissions section of the docs, you might have to ask your webhost for support if you have no idea what permission level you need, as this differs from webserver setup to webserver setup. This isn't something that we could possibly help you with. Many users ask why this has to be so complicated, because the permissions concept on (mostly Linux-driven) webservers is alien to them. They blame the coppermine devs for this process being so complicated. Well, simply put: we can't make it easier for you. The coppermine script (or any PHP-driven script) doesn't have the powers to change the permissions. From the
preliminary documentation for cpg1.5.x (that apply in this case to cpg1.4.x as well):
Asking for support on permissions issues
Most users who come from a Windows-background (or who have no idea about how permissions work at all) frequently ask on the Coppermine support board "Why does this have to be so complicated? Why don't you just create a script that handles all those complicated permission issues for me?". The answer is pretty straightforward: because we can't.
Coppermine has been built to work on a number of platforms and operating systems. The permissions that you need to set are part of how the operating system of your webserver works - they are not related to Coppermine in itself. A script can't assign permissions to itself if it doesn't have the privilege to do so. Think of it as if it was the structure of an army: a soldier who is low in rank can not promote himself to be a general; only officers who actually have higher privileges can promote regular soldiers to a higher rank. They wouldn't make them a general in the first place though, but just give them the rank they need to do their job (i.e. they would promote a private to corporal).
As the setup of webservers differs, we can't give you a simple, straightforward instruction like "CHMOD everything to 755 and you'll be done". Although this may be the case for many on shared webhosting, it might not apply to you. On some server setups, it might not be enough. On others, it might be a security risk. Yet on another machine, it may not apply at all because there is no such command.
Supporters are reluctant to answer the same questions on permissions over and over gain, as they are not related to Coppermine in the first place. If you ask a permissions-related question on the Coppermine support board that clearly shows that you haven't read the documentation (at least the part that covers permissions), then you will probably get a harsh answer, or no answer at all. Please think twice, read the permissions section carefully. There's little others could do to help you on this. If you're really stuck, you better ask your webhost for support.