How can i remotely access server that is on a private network

I am living in an apartment complex with free wireless Internet and i turned this old pentium 4 computer into a web/media/file server. I want to be able to access my server away from home but i am extremely limited and i can not forward ports and I have no other kind of network privileges. I am a complete idiot when it comes to networking solutions and I am trying to learn. I have a very vague understanding of vpns and dynamic dns services but i do not understand what i need to access my server from a different network. I setup dns services for my home server but still have not been able to resolve hostnames to actual y point to my server or maybe my networks firewall is blocking me. I also have a DD-WRT wireless router currently running as a repeater and I do not know if i can use this device to help me accomplish my objective. I am confused and stuck and if anyone could point me in the right direction i would be extremely thankful.