internet dies off only in night

im using airtel broadband connection, its a scheme where from 10pm till 8am in morning i can download unlimited, and the funny thing is the net doesn't work from 10pm till 8am which is granted as free download time.
they've given me beetel 110BX1 ADSL2 + ROUTER
initially i thought its problem from my computer so i removed the lan card and used on board card - re-installed drivers - the modem shows connected, all the lights on it are solid, while normally the last 2 are blinking, only way to use net ( temporarily ) is to restart modem + computer and if im lucky and with god's grace net might work for more than 1-2 hour.
i recently re-installed os and there is no virus in computer. Is the problem from my side or their side, they already promised to solve problem within 24 hours but its not yet done.
I'll be speaking to their senior tech executive and i don't want to sound like a nooby, please let know what u guys over this.

P.S - sorry for my horrible english

try pinging your default gateway, if it works then it is probably they have a problem and they should fixed.

You can do as advised by Alan. If you can able to ping the default gateway, then also try to ping any web site e.g yahoo.com, google.com.
If you can able to ping yahoo, google means internet connection is ok

Do you have to restart both your computer and router/modem? Or can it work some times when you restart only the router or only the computer?

Trying here to narrow down the problem.

its random- sometimes i need to restart only mode, sometimes need to restart modem + comp + plug out n in lan wire
yesterday he changed the modem and gave me a wireless router ( maybe he ran out of stock of adsl modem )

When it happens again, try to ping your gateway IP as Alans said (you can know it by typing ipconfig /all in command prompt). If it doesn't reply (timed out), then the problem could be that the router/modem is probably hanging for some reason. If the gateway replies to the pings, then it could be a NAT or routing problem. In both cases , it's configuration needs to be investigated.

There is another scenario that the gateway might not reply but the error displayed is not a "Request Timed out" but some thing like "Hardware error" or "Destination host unreachable", in this case the problem could be in your computer, but not for sure.

Tel us what happens.