The company who removed the server should really have informed you about what happens when a domain-joined computer has no DC to contact and some of the things you'll notice you can or can no longer do since the computer is still part of a domain...
It shouldn't harm anything by keeping the machine as part of a domain, however, it makes no sense to keep it on a domain if you have no domain controller to manage the trust between your computer, the DC and the other computers on your domain.
It would be easier to remove the computer from the domain and you will then have a standalone machine as you originally purchased. You will also lose any Group Policy settings and security groups that the domain provided.
To remove the computer from the domain all you need is a local administrator username and password to put the computer back into a Workgroup.
- Right click
Computer name, domain, and workgroup settings click
Change settings - you will need to have the local Administrator account details to hand
- A new window will open with some tabs - Click the first tab
rename this computer or change its domain or workgroup
- Select the
Workgroup radio button
- Enter a workgroup name - you will need to re-use this on the other computers
- You may be asked to provide local Administrator account details again
- When the computer is joined to the new workgroup you will be asked to restart your computer - do so as this is crucial.
- Repeat for each computer on your LAN
To then be able to share files on your new workgroup - especially with Windows Vista, 7, 8, 8.1 and 10 - you should create a HomeGroup where this will allow you to share files if you keep them on your LAN. You have cloud storage so if this works well for you then keep using this.