Whats the best way to check if there is problem with dedicated provider's network??

I did a ping test with IPs from my pc...
But I keep getting "request time out" like every 5 lines...
Then I got a few customers complaining the Website/FTP speed too....So I guess there must be something wrong...

Try running a traceroute, if it quits on the last hop, then you know it's a (pretty bad) ICMP block. If not, then it's a network problem. Also, make note of the last IP address in the trace that worked and run a Whois lookup on it, www.arin.net.

You could set-up monitor w/ a 3 party to give you good info.