Dropbox.com not accessible on Yosemite 10.10.3
For some reason your connection time is very long.

Lets test it.

Open the Terminal app located in your Utility folder.

Now type Ping dropbox.com

It should come back with something like this 


  PING dropbox.com (108.160.172.232): 56 data bytes
  
  64 bytes from 108.160.172.232: icmp_seq=1 ttl=51 time=19.474 ms


I have about 15 to 20 milli seconds (ms), you are showing few hundreds ms (500). that is definitely not good.

Based on your results you have a Ping (some Internet address) problem while your Internet speed is very good.

Usually that comes from the DNS (Domain name Server), not resolving the Internet address correctly/Fast.


First lets clean your DNS cache, just in case something is stuck in there.


Use Terminal and run sudo discoveryutil mdnsflushcache enter your password when asked. Now you should have a clean cache and can start over.


Next would be to run a trace route (to Dropbox) to see where is it going and where it takes forever. In Terminal type Traceroute Dropbox.com and wait for it to finish (it takes few moments.
The first line is to your router and it should be less the 1 ms (I have 0.7 ms). The following lines are other routes (you can see the names of the servers). I end up with 30ms to the dropbox.
Lets carefully check your Network settings step by step.


TCP/IP -Use DHCP

DNS- we discussed that (but take note how many you have in there and what they are)

Proxies- they should be all off

Hardware- Automatic (MTU-Standard 1500)


Lets see who is using your Internet. Turn off programs like Mail, Browser, Skype ect. to make that a short list.


Now type lsof -i -P in Terminal and look who is still using your Internet.


There is a small application/Script that will evaluate all DNS servers around you and recommended which one is fastest for you to use. Give it a try, I use it and it does help with the DNS stuff.
The following is to just check the content of your Host file. Follow the instructions here to test your Host file setting.