Have you tried doing a traceroute from inside the school network to see if you can determine where the packets are dropping off?
As a frame of reference, from my location I get:
C:\>tracert
Tracing route to gabe.cd.pvt.k12.oh.us [198.234.201.99]
over a maximum of 30 hops:
1 <10 ms <10 ms <10 ms border [192.168.0.1]
2 <10 ms <10 ms <10 ms <removed for security> [12.107.XXX.XXX]
3 <10 ms <10 ms 16 ms <removed for security> [207.252.XXX.XXX]
4 <10 ms 15 ms 16 ms <removed for security> [207.252.XXX.XXX]
5 <10 ms 16 ms 15 ms <removed for security> [207.252.XXX.XXX]
6 16 ms 46 ms 16 ms 12.125.120.37
7 15 ms 16 ms 16 ms gbr2-p27.cgcil.ip.att.net [12.123.193.70]
8 16 ms 31 ms 16 ms tbr2-p013602.cgcil.ip.att.net [12.122.11.53]
9 16 ms 15 ms 16 ms gbr5-p40.cgcil.ip.att.net [12.122.11.58]
10 16 ms 16 ms 31 ms gar2-p360.cgcil.ip.att.net [12.123.5.217]
11 16 ms 31 ms 16 ms 12.125.142.34
12 * * * Request timed out.
13 * * * Request timed out.
14 * * * Request timed out.
15 * * * Request timed out.
16 32 ms 31 ms 31 ms gabe.cd.pvt.k12.oh.us [198.234.201.99]
The only interesting thing I notice from the outside is that something is blocking my ping packets at hops 12 through 15. It could be a firewall sitting in front of those devices, or the devices themselvs may be filtering out the packets.
If you do the traceroute and sucessfully get out of your network before the trace fails, I would start to suspect that there is a firewall or router dropping your packets before they reach the site.