To help clarify a little. It sounds like your parents are using an ADSL connection or similar?
You need to connect as follows:
[Parents PC] <------> ( INTERNET ) <------> [Your PC]
Easiest thing to check 1st is that you are able to connect to someone else. Ask a friend to help you test locally - I.e. someone who lives near you, that way you can confirm that it isn't a problem at your end. It may be that you have a router locally blocking the traffic.
Once you have ensured that you are able to connect ok over the port listed then ensure that both sides are connected to the net ok.
Then once you are happy that all is in order - Check that you can connect over telnet as described above. Step by step details here:
1) Check parents IP - If unsure how to find public IP there are plenty of sites:
to name a couple, which will show their IP - Get them to take a note of it.
OR
if they are confident enough they can use a program called ipconfig (Start - run - type cmd & press enter - type ipconfig & press enter - read the line titled IP ADDRESS)
2) Once you know their IP - on your own pc do the following:
Click on START - RUN - Type: cmd & press enter - Type: telnet parentsIP 3389
Example: telnet 127.0.0.1 3389
A black screen shows a connection is made & is a good sign. if not then post back here to let us know how you got on.
Good Luck