Does it have a timming belt - 2004 Hyundai Elantra

Sounds like you have installed the belt out of time. Check your alignment marks and re-install the belt.

you might want to check to see if you got a timming chain or belt in that car.
but check that area first .
could be a broken timming belt.
you need to remove the dust cover in that area .
check for no belt present on the timming gears.
good luck,Gary

Well it is an interference engine which means if the belt breaks the pistons could damage the valves.
If it only jumped a couple of teeth it may not have damaged anything.
I would put a new belt on and check compression.

Its possible the gears are not on the right marks.
Have you checked cam timing since replacing the second belt ?

Timing belts don't while because they don't slip! Could be the water pump/alternator belt.

I found this diagrham, by what I read, be very careful NOT to rotate any pulleys when the belt is off and put little arrows on the pulleys and belt in the same spots and flowing in the same direction to aid yourself when it is being replaced.

a stripped group of cogs on timming belt is most likely ur problem,a new timming belt may not solve ur problem,this is a interference engine ,u may have bent vavles,install timming belt and if it runs,and runs smooth and got plenty of power,then u will be ok

There is no room for error...... Zero clearance. If off one tooth it can and will bend valves. if you are one that just feels the need to get alittle dirty or just can't pay for the service, then get out your Haynes out and turn to .....Tune up, and look at replacing timming belt. Get a cam gear tool that locks them into place so as that they will not move when u have them lined up. make sure they are lined up with marks as said in book. then make sure crank as well as all marks are lined up acordingly. make sure belt marks are lined up with everything. i would reccomend using a volvo belt though cause it will have all the marks on it.However other company's make good quality belts also at a fraction of the price. So it is really up to you.
Good thing when doing timming belt is to also change out your timming belt tensioner. YES do this it will save you a engine in the long run. it is a moving part that will go bad, it will freeze up and snap timming belt. rip out teeth in thebelt and bend valves. So as a gen rule...When you change timming belt, Change belt tensioner at same time since you cant just change tensioner without changing or getting timming belt off. Remember to use your HAYNES. It is your friend and will save you money in the long run. Good luck... Hope this helps you.

The problem is else where,they have enclosed t/chain,the belt drives the water pump,altinator,power steering etc.,The engine should be checked by a professional for other problems,should not be driven or run without the drive belt in place.

REMOVED ALL BELTS, WATER PUMP FAN, SHROUD AND PULLEY.
REMOVE TIMING COVER REMOVE CRANK SHAFT PULLEY.
. PUT ENGINE IN TOP DEAD CENTER SO YOU CAN SEE TIMING MARKS. REVERSE PROCEDURE. GOOD LUCK