Since this is a new laptop, you probably have Vista or maybe Windows 7 installed, in which case, DOS graphics won’t work. You can install DOSBox and run you applications there, at a performance cost. Once you’re past that problem, SVGA256.BGI should work for you.
As a side note, this forum is not the right place to post questions about DOS graphics. You will probably get more help elsewhere.
Unfortunately, you won’t find any BGI files from Nvidia, so far as I know. I have previously used SVGA256.BGI and the others in Turbo Pascal on Windows XP, but not mini XP (never heard of that one in fact :) ). I was also using an ATI Mobility Radeon 9250 back then, so I don’t know if this is something Nvidia just doesn’t support any more.
I would suggest the following:
Google all of those BGI files, download a few versions and try each one - maybe there is a bug with the particular one you are using. I don’t have high hopes for this option though.
Search for VESA (Video Electronics Standards Association) SVGA libraries. There are a number of people who have implemented their own 2D graphics libraries that use SVGA graphics but don’t use BGI files. They rely on interrupts to communicate with graphics hardware and should still work as long as mini XP allows your program to use those interrupts.
You are using tools from more than 10 years ago. Can you convince your teacher to use something newer, like OpenGL or DirectX?
I have just tested DOSBox with some old Turbo Pascal programs that use BGI files and it works. This will probably be your best, easiest solution. DOSBox gives you a command prompt from which you can run Turbo C and your applications. This still works under Vista 32-bit (just tested), so it should work for mini XP too.