Question : Exchange 2007 has stopped working

We have an Exchange 2007 setup running on Server 2003 R2.  Over the weekend this has failed with Outlook clients showing 'disconnected' and OWA unable to access. All services are running and invetsigation has shown that the M drive has run out of disc space - due to 94GB of log files not being cleared down by the backup software on the server (Windows Backup).  We are currently running a full manual backup (ie NOT the backup everything on the computer option) and have confirmed that the Exchange information store is selected to be included, along with system state.  This will take at least 12 hours to complete.
There is also an old expired transport certificate (expired 2008) that the event log is complaining about.

Questions are:
1. Why has Windows Backup failed to clear down the log files in previous backup ?
2. Could anything else have caused this problem ?

The error report from an attempted OWA logon states: (domain and IP details changed)

Request
Url: https://webmail.site.area.org.uk:443/owa/default.aspx
User host address: 1.2.3.4

Exception
Exception type: Microsoft.Exchange.Data.Storage.ConnectionFailedTransientException
Exception message: Cannot open mailbox /o=MyDomain/ou=First Administrative Group/cn=Recipients/cn=CurrentUser.

Call stack

Microsoft.Exchange.Data.Storage.ConnectionCachePool.OpenMailbox(String serverDn, String userDn, String mailboxDn, Guid mailboxGuid, Guid mdbGuid, Object identity, ConnectFlag connectFlag, OpenStoreFlag openStoreFlag, CultureInfo cultureInfo, String clientInfoString, Boolean secondTry)
Microsoft.Exchange.Data.Storage.ConnectionCachePool.OpenMailbox(String serverDn, String userDn, String mailboxDn, Guid mailboxGuid, Guid mdbGuid, Object identity, ConnectFlag connectFlag, OpenStoreFlag openStoreFlag, CultureInfo cultureInfo, String clientInfoString, Boolean secondTry)
Microsoft.Exchange.Data.Storage.ConnectionCachePool.OpenMailbox(String serverDn, String userDn, String mailboxDn, Guid mailboxGuid, Guid mdbGuid, Object identity, ConnectFlag connectFlag, OpenStoreFlag openStoreFlag, CultureInfo cultureInfo, String clientInfoString)
Microsoft.Exchange.Data.Storage.MailboxSession.Initialize(LogonType logonType, ExchangePrincipal owner, DelegateLogonUser delegateUser, Object identity, OpenMailboxSessionFlags flags)
Microsoft.Exchange.Data.Storage.MailboxSession.CreateMailboxSession(LogonType logonType, ExchangePrincipal owner, DelegateLogonUser delegateUser, Object identity, OpenMailboxSessionFlags flags, CultureInfo cultureInfo, String clientInfoString)
Microsoft.Exchange.Data.Storage.MailboxSession.Open(ExchangePrincipal mailboxOwner, WindowsPrincipal authenticatedUser, CultureInfo cultureInfo, String clientInfoString)
Microsoft.Exchange.Clients.Owa.Core.OwaWindowsIdentity.CreateMailboxSession(ExchangePrincipal exchangePrincipal, CultureInfo cultureInfo)
Microsoft.Exchange.Clients.Owa.Core.UserContext.Load(OwaContext owaContext)
Microsoft.Exchange.Clients.Owa.Core.RequestDispatcher.CreateUserContext(OwaContext owaContext, UserContextKey userContextKey, UserContext& userContext)
Microsoft.Exchange.Clients.Owa.Core.RequestDispatcher.PrepareRequestWithoutSession(OwaContext owaContext, UserContextCookie userContextCookie)
Microsoft.Exchange.Clients.Owa.Core.RequestDispatcher.InternalDispatchRequest(OwaContext owaContext)
Microsoft.Exchange.Clients.Owa.Core.RequestDispatcher.DispatchRequest(OwaContext owaContext)
System.Web.HttpApplication.SyncEventExecutionStep.System.Web.HttpApplication.IExecutionStep.Execute()
System.Web.HttpApplication.ExecuteStep(IExecutionStep step, Boolean& completedSynchronously)

Inner Exception
Exception type: Microsoft.Mapi.MapiExceptionLogonFailed
Exception message: MapiExceptionLogonFailed: Unable to open message store. (hr=0x80040111, ec=-2147221231) Diagnostic context: Lid: 18969 EcDoRpcExt2 called [length=443] Lid: 27161 EcDoRpcExt2 returned [ec=0x0][length=132][latency=46] Lid: 23226 --- ROP Parse Start --- Lid: 27962 ROP: ropLogon [254] Lid: 17082 ROP Error: 0x80040111 Lid: 26937 Lid: 21921 StoreEc: 0x80040111 Lid: 27962 ROP: ropExtendedError [250] Lid: 1494 ---- Remote Context Beg ---- Lid: 26426 ROP: ropLogon [254] Lid: 22787 Error: 0x0 Lid: 13032 StoreEc: 0x8004010F Lid: 59409 Lid: 45073 Lid: 11173 StoreEc: 0x80040111 Lid: 22970 Lid: 8620 StoreEc: 0x80040111 Lid: 1750 ---- Remote Context End ---- Lid: 26849 Lid: 21817 ROP Failure: 0x80040111 Lid: 26297 Lid: 16585 StoreEc: 0x80040111 Lid: 32441 Lid: 1706 StoreEc: 0x80040111 Lid: 24761 Lid: 20665 StoreEc: 0x80040111 Lid: 25785 Lid: 29881 StoreEc: 0x80040111

Call stack

Microsoft.Mapi.MapiExceptionHelper.ThrowIfError(String message, Int32 hresult, Int32 ec, DiagnosticContext diagCtx)
Microsoft.Mapi.ExRpcConnection.OpenMsgStore(OpenStoreFlag storeFlags, String mailboxDn, Guid mailboxGuid, Guid mdbGuid, MapiStore msgStorePrivate, String& correctServerDn, ClientIdentityInfo clientIdentityAs, String userDnAs, String applicationId, CultureInfo cultureInfo)
Microsoft.Mapi.ConnectionCache.OpenMapiStore(String mailboxDn, Guid mailboxGuid, Guid mdbGuid, ClientIdentityInfo clientIdentity, String userDnAs, OpenStoreFlag openStoreFlags, CultureInfo cultureInfo, String applicationId)
Microsoft.Mapi.ConnectionCache.OpenMailbox(String mailboxDn, Guid mailboxGuid, Guid mdbGuid, WindowsIdentity windowsIdentityAs, String userDnAs, OpenStoreFlag openStoreFlags, CultureInfo cultureInfo, String applicationId)
Microsoft.Exchange.Data.Storage.ConnectionCachePool.OpenMailbox(String serverDn, String userDn, String mailboxDn, Guid mailboxGuid, Guid mdbGuid, Object identity, ConnectFlag connectFlag, OpenStoreFlag openStoreFlag, CultureInfo cultureInfo, String clientInfoString, Boolean secondTry)

Answer : Exchange 2007 has stopped working

Is DNS is working on your server? Check it please.