I have a Sharepoint 2010 farm with 2 frontend server and 2 backend server.

We have a huge problem because some old admin deleted the msi files located on winsxs folder in all 4 servers. Im unable to install any SharePoint service pack and Microsoft dont support this kind of problem.

I need to rebuild my entire installation in new servers, but i dont know if i should gradually add servers to the farm and remove the old ones or if I should backup everything and restore it elsewhere. I know there are probably pro and cons in each option, but unfortunately im still learning how SharePoint work. (My company signed a new contract for SharePoint support and dont help the team to learn to support the tool)

Any help is appreciated. Sorry for my bad english.

I would add new servers to the farm and slowly de-provision the old servers.  You could backup everything, but that will probably lead to more downtime to get the new environment up and running.

Hi

i agree with Paul's answer

but you could as you said in a new created farm ( same 2010 version ), a new topology if necessary, then migrate Content DBs to the new env. This way no issues on prod env will occure

Take as an option upgrade from 2010 to 2013 platform,   build a new farm ( upgrade from 2010 - only dettach/attach DBs )

I hope the above suggestions clarifies your concern to get this job done.

Moreover, you may also have a look on below given informative resources that might helps you to get in more details.

Backup your old sites using Backup-SPSite powershell command and restore the backup file on the new server using Restore-SPSite command.

http://technet.microsoft.com/en-us/library/ff607901.aspx

http://technet.microsoft.com/en-us/library/ff607788.aspx

Simple Guide to Moving SharePoint Content Databases to a New Server: http://sharepointpromag.com/sharepoint-administration/simple-guide-moving-sharepoint-content-databases-new-server

How do I migrate a SharePoint 2010 site to a new server and new SQL instance: http://serverfault.com/questions/161879/how-do-i-migrate-a-sharepoint-2010-site-to-a-new-server-and-new-sql-instance

You may also try this solution ( http://www.lepide.com/lepidemigratordocuments/sharepoint-to-sharepoint-migration.html ) which lets you to migrate content between SharePoint servers.

Hope it helps you!