Internet cable not working on other pc?

I have 2 laptop and 2 internet connection
laptop 1 = lenovo g560 i3, 2gb memory working fine
laptop 2 = the same as laptop 1 but has higher [ memory, HDD, vcard] working fine

internet 1 = dsl connection 1mb, modem with Wi-Fi with 4 extra pc ports [ provided by isp]
internet 2 = dsl connection 1mb, his modem is like a direct., 2 ports, the cable that goes to internet and cable that goes to pc.,.

so internet 2 was installed and the pc they use is laptop 1.,

so here i'm at internet 2 place, i brought my laptop 2 and used internet 2 and plugged on laptop 2.

but it says no internet connection, it have a exclamation mark.,
but when i plugged it on its original pc[laptop 1 ] it works.,

i already tried plugging laptop 2 using internet cable on internet 1 and it works properly, so when internet 2 doesn't work on laptop 2 i assumed that internet 2 is at fault.,

so my question.,
is internet 2 only usable on laptop 1?
cuz i want internet on laptop 2., and i can't cuz i don't have Wi-Fi only way is to borrow the internet 2 to laptop 1.

Driver issue, perhaps… That is a very unitelligeble question