You can trick your browser into resolving the domain to the hosts IP by creating a hosts file entry ...
OK, it's great that you knew the address ! It proves that the hosting is still working, and a whois on the address shows that the hosting is with RapidSwitch.
As it's an area I sort of deal with in the day job, perhaps I can explain what's needed now - and what'll happen if it doesn't happen.
Getting hold of the domain name itself is one task. Unless someone knows the registrant, it's going to be difficult - it's marked as transfer prohibited because they don't allow domains to be transferred when they are in this limbo state between expiring and being deleted. So it either has to be renewed and then transferred to someone who is prepared to take ownership, or ...
You wait for it to be deleted, and then re-register it. The problem there is that there are professional squatters who have automated systems to buy up such domains so they can then extort ..., err I mean sell it to whoever is prepared to pay the price they set. With something popular and with good search engine rankings (as this probably does), they'll smell the money.
Not sure what can be done about that. If it can be re-registered before the squatters get hold of it, then it's looking rosy.
The hosting is separate. Deleting the domain does not automatically delete the hosting - though that can be different when both are with the same people. So just renewing the domain and resetting the DNS would get the site back up and running.
The next issue is keeping the hosting running, and that will mean paying the hosting company - as well as getting admin access to the site in order to manage it.
Without paying for the hosting, at some point the account will expire and the hosting company will delete the whole lot. If we could somehow pay for it, but not get admin access, then it would carry on running until something went wrong.
Sadly, with personal commitments right now I have little time, and even less money to put into it.