Vista - Network card sometimes works, sometimes not

There was already one network card integrated on the motherboard, but
I installed another network card and its drivers. The problem is that
connecting the cable from the ADSL modem to this network card, the
Internet connection is not usually established. Instead, Vista
complains that it hasn't found any wireless connections. Doesn't it
look for wired connections? Occasionally, however, the connection does
form.

Are IRQ conflictions possible on modern machines?

Btw, are "Ethernet" and "Gigabit" standards compatible with each other?

Most likely you need to go into the BIOS on start-up and disable the onboard
network card in order to use your add-on card, presuming that both the
motherboard and add-in card are for wired ethernet. There should be no
problems if your add-on card is wireless only.
In truth you will not see any real performance gains from an add-on card
compared to the motherboard network device unless you are moving to a full
bore gigabyte network, in which case you should already know the answer to
your problem.