The bandwidth of a network card would generally outclass your internet connection by an offer of magnitude.
Gigabits per second network cards have been standard for at least a decade.
And then there’s your wifi too, if applicable, but even that is much faster than your general internet connection.
A new laptop, even the best in the world, won’t make your downloads any faster.
I also back what everyone else is saying. Unless of course you can update your current laptop. What have you got? An extra stick of ram and an SSD can make an old laptop feel brand new, especially with an OS reinstall