as bob says, you'll want to look (probably paste here) relevant sections of your alfresco.log and/or catalina.out. When I've had that error ("The remote server may be unavailable or your authentication details have not been recognized.") the reason is either:
1. I'm trying to log in to /share but /alfresco did not start correctly. share talks to alfresco. so share may start up (you can see its login screen) but you can't actually login since alfresco didn't start so share can't auth.
2. you may have modified the authentication chain (e.g., your previous alfresco may have been using active directory or LDAP auth or even passthru).
to see which is the case, first browse to /alfresco. If that doesn't work (you DO NOT see the /alfresco login screen there) then you have problem #1 above. paste your log files (or look at your log files for errors and paste those).
If you *DO* see the /alfresco login screen then your old alfresco had customizations that your new alfresco doesn't have. I would probably copy the whole of tomcat/shared/classes over from the old alfresco to the new. most of the changes you'll need will be in alfresco-global.properties, but there might be some subsystem specific config in alfresco/extension/subsystems too.
If that still doesn't work, then you'll need to understand your system more completely (and describe it more completely here). e.g., you might be using kerberos or some sort of SSO configuration at apache level, etc.
In future, you should always have a staging or development server. You test things on staging before deploying to production. You also test your backup and restore on staging (run backups on production, and every week or every month, take a current backup and restore it to staging, make sure that your backups CAN BE RESTORED.