Hi BigChimp, Ludob, Eny, and thanks everyone for replying/helping.
I think I have found what I was after, and even more as offered by Thinkgrid:
http://www.thewhir.com/web-hosting-news/cloud-firm-thinkgrid-launches-microsoft-windows-7-hosted-virtual-desktopsThey offer business solutions consisting of virtual Windows7 desktops that are accessible via the web.
One can put his own applications, and from any where, any pc, used one's virtual PC. Connections are secure, response is said to likely faster than if one is using local machine.
For instance, if I were to put an SQLite database there, and put the lazarus application.exe there too, even with large amounts of data, it would run EVERYTHING THERE, while I watch and interact requests from my local PC. Plus, it'd likely run faster than on my local PC.
I can also install on that virtual PC the PostgresQL server and hit it with apps installed on that local machine, so in a way, seems to me, I would have a web-based SQL server too, with likely not much different than having a web-hosted sql server.
In addition, anyone else who wants to group into the account, would have to have his private virtual machine, in the same manner, and there is a common folder that can be accessed by those grouped.
Part of the beauty is that the real local machines have nothing to do with the processing power of the virtual machines, and can be run from linux, and other operating systems.
This mode IS NOT a public model, which even fits my thoughts better. It is a business model, which is the reason for my o.p.
I am impressed with it, and off to verify things via a free trial. Costs seem reasonable, specially for business solutions.
Thanks everyone!
This is a very convincing video on the Virtual Windows7 desktops:
http://hvdi.com/video/8x6-30JuneHVDthinkgrid/8x6-30JuneHVDthinkgrid.htmlP.S.: They also have exactly what I was asking for:
Hosted File Server
An alternative to a NAS box or office file server. A hosted file server is delivered securely from ThinkGrid's data centres and provides exactly the same experience as having the file server in your office. The only difference is that it can be accessed anywhere by anyone you wish to grant security clearance to, and we provide backup, security and archiving for your data so it will never be lost.
http://thinkgrid.com/file-collaboration-hostedfileserver.aspx