domain name not working?

What is the domain name and what is the IP address?

It seems like a DNS problem at your server, but why you said:
 " Is this some kind of issue because I'm logging in as root on this computer and server doesn't let me connect twice? "
Do you want to connect to your server from your server using the domain name inside a browser?
However, can you please open a terminal and run:
 ifconfig -a
and then paste here the output.
Which Ubuntu version are you using? and the Apache version?

Hey, thenks for answers, ifconfig -a:

eth0 Link encap:Ethernet HWaddr 00:14:38:12:17:29
          inet addr:89.212.214.247 Bcast:89.212.255.255 Mask:255.255.0.0
          inet6 addr: fe80::214:38ff:fe12:1729/64 Scope:Link
          UP BROADCAST RUNNING MULTICAST MTU:1500 Metric:1
          RX packets:15053 errors:0 dropped:0 overruns:0 frame:0
          TX packets:17467 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:1000
          RX bytes:4030093 (4.0 MB) TX bytes:13398833 (13.3 MB)
          Interrupt:16

lo Link encap:Local Loopback
          inet addr:127.0.0.1 Mask:255.0.0.0
          inet6 addr: ::1/128 Scope:Host
          UP LOOPBACK RUNNING MTU:16436 Metric:1
          RX packets:313 errors:0 dropped:0 overruns:0 frame:0
          TX packets:313 errors:0 dropped:0 overruns:0 carrier:0
          collisions:0 txqueuelen:0
          RX bytes:27732 (27.7 KB) TX bytes:27732 (27.7 KB)

Im using Ubuntu server 8.1, Apache2

^^ but now the interesting part is, im somehow able to access domain with www.downbase.net but downbase.net (without www.) isnt working, even though i entered it at my DNS service. Is this DNS or apache problem then? :S

Thenks again...

I made this test using your dns server

dig @89.212.214.247 www.google.com

; <<>> DiG 9.5.0-P2 <<>> @89.212.214.247 www.google.com
; (1 server found)
;; global options: printcmd
;; connection timed out; no servers could be reached

Here my dns server... answer ( i have changed the original dns ip in the answer )

dig @55.155.56.250 www.google.com

; <<>> DiG 9.5.0-P2 <<>> @55.155.56.250 www.google.com
; (1 server found)
;; global options: printcmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 18305
;; flags: qr rd ra; QUERY: 1, ANSWER: 5, AUTHORITY: 4, ADDITIONAL: 0

;; QUESTION SECTION:
;www.google.com. IN A

;; ANSWER SECTION:
www.google.com. 242043 IN CNAME www.l.google.com.
www.l.google.com. 175 IN A 74.125.79.103
www.l.google.com. 175 IN A 74.125.79.104
www.l.google.com. 175 IN A 74.125.79.147
www.l.google.com. 175 IN A 74.125.79.99

;; AUTHORITY SECTION:
google.com. 155663 IN NS ns1.google.com.
google.com. 155663 IN NS ns4.google.com.
google.com. 155663 IN NS ns3.google.com.
google.com. 155663 IN NS ns2.google.com.

;; Query time: 175 msec
;; SERVER: 55.155.56.250#53(55.155.56.250)
;; WHEN: Sun Jan 25 16:26:45 2009
;; MSG SIZE rcvd: 188

Hi,
The real domain name is without www, to get your site be accessed through www you must configure it as a subdomain.
As I can see you are doing the hosting of your website by yourself, from the outside of your network (where I'am), your site is visible using any method (IP, www.downbase.net or downbase.net) and this means that your DNS server configurations are 0K.

Let me explain a little more.
As marcobra said, you don't have a public DNS server mounted at your location (Ubuntu server), but it's recognized from Internet (It means that you have successfully configured your authority name servers at your DNS service provider).
Generally speaking your router/gateway should get an IP address from your ISP. With that it should get the DNS servers addresses. Most then run DHCP to the internal network and tell the clients (your pc) the DNS servers to use, and to use the router as the default gateway. If this isn't working properly then you can set the DNS servers in the file /etc/resolv.conf. Edit this using the following:-

$ sudo gedit /etc/resolv.conf

Then make sure there is an entry for each nameserver in the format below

nameserver <ip address of nameserver 1>
nameserver <ip address of nameserver 2>

or paste their content here and we'll see if something is wrong with that (if we can).
However, if you want a DNS server at your location, you can go to the following link:
http://www.ubuntugeek.com/dns-server-setup-using-bind-in-ubuntu.html
or many other sites explaining haw to setup a DNS server.
Hope this help, let me know.