DSL with 2 Computers

I just got DSL for my office. I have 2 computers in my office. I have a small ($5) splitter that I have tried to use to stick into the DSL modem and then have 2 ethernet cables coming out (each to one of the 2 computers).

Only one computer is online at a time. It's the computer that is in the splitter side labelled "#1", the other one, labelled "#2" is not working.

When i switch the cables, the other one works. So it seems that it's only working with whichever computer is in the splitter side labelled "#1"

How can I fix this? I really don't want to buy a router.

Penny wise and pound foolish -old proverb

You didn't do your homework. If you had you would have learned that your ISP only gives you ONE IP ADDRESS. Just splitting the signal is only HALF of the issue.

You could

1. purchase an additional ip address from your ISP [years worth of fees could pay for a router]
2. put in a wireless router [easiest and quickest solution]
3. put in a 2nd nic card in one of the pcs. One card connected to the internet, one with a crossover cable to the other pc. Use ICS [internet connection sharing] setup on the primary pc to give internet access to the second pc. [depends on how good your are at networking could cost you lots of hours and frustration]

Best of luck!