Can I still use old cards?

I am getting back into the game and I have a bunch of old Jyhad cards that I had back when the game first started. Am I still able to incorporate and play with these cards with the new game system?

Sure can! A lot of those cards are still the same, and very much playable.
As a courtesy, when mixing different card backs it’s probably best to use opaque sleeves to hide the backs.
Some cards have changed, so do a quick check using something like Amaranth to see if it matters to your cards. A few cards were banned, so peek at the banned list too (Amaranth will point this out).
Other than that you only have to abide by the crypt grouping rules described in the rule book (Jyhad backed cards are all group 1).

This is one of the many facts, why VtES is such a cool game.

Old cards are tournament legal, as long as you use opaque sleeves. (the card backs have changed couple times from Jyhad)

Be however aware that many cards have received errata over the years. You might want to check the most up-to-date wordings here:
www.vekn.net/images/stories/downloads/cardlist.txt