Internet connecting problems

Hi, everyone, i'm a beginner in networking and Internet access, so please bare with me.

I got an Internet connection about 5 months ago. It was ok for a couple of months, but then it started to malfunction.

Let me first explain the situation shortly:

I am part of a Local Area Network -- about 25 computers. We all have virtual IP addresses. (192.168.100.1 --

192.168.100.30, with a 255.255.255.0 mask). The guy with the Internet came and made 192.168.100.1 the gateway for all

of us.
When I do a tracert URL, i see the following hops:
1. 192.168.100.1
2. 10.10.10.1
3. *
I was told the router echoes all my ping and other requests so that's why I can't see further more. The important thing

is that 10.10.10.1 is the next step to my Internet connection.
Now this is where I get my Internet from, as far as I'm concerned.
But, as I said, lately it does not work. Everyone else on my LAN has a running Internet connection and I don't.
I ping 192.168.100.1 and it has good reply (the lan is ok).
I ping 10.10.10.1 and I get Request timed out.
Whenever my Internet connection is ok, I get good ping reply from 10.10.10.1.
What could be wrong that my connection does not work? I have fresh installed Windows 2000 SP4.
Also I noticed that right after I restart my computer the 10.10.10.1 ping reply is good, and then in a couple of

minutes starts timing out replies.

Please help me with some advice, I really need Internet connection for my school research.
Is it my computer's fault, or the router's?

I would imagine that since every other computer in the network can still access the Internet and you can't, that the problem is related to your computer. Have you done anything to your computer that could have caused this change? When you can't ping the router, do you lose all other network connections, or can you only not access the router? Perhaps it's a faulty NIC or cable.