Does my 2004 hyundai tiburon have a timming belt or chain? when do i have to change it

I would suggest you get a good mechanic to do this for you. Some versions of the Tiburon 2.0l have an over complicated setup with belts and chains and getting the set up wrong could be painfully expensive.

the hyundai tiburon v 6 1999-2008 has a timing belt and is an intereference engine which valve damage will occur if belt breaks or correct belt replacing procedure is not followed
belt changing interval is 60,000 milesor multiples thereof or 48 months which ever comes first

Follow the link to a complete guide to replacing the timing belt on your engine http://www.newtiburon.com/forums/diy-engine/192520-2-0l-timing-belt-replacement.html

It will probably be a worn belt, examine belt for cracks and shiney spots.
You can buy a spary belt conditioner from the parts store but I would suggest replacement

Btw, I’m available to help over the phone in case u need at https://www.6ya.com/expert/jason_77a19afa8d604dee

it could be anywhere from 500.00 to 800.00 dollars

Usually plugged fuel filters and/or bad pumps cause loss of power at the high end (full throttle) when you are sucking down the fuel not so much at the low end.

Rough idles can be a lot of things, usually something to do with the fuel mixture or timings. Dirty injectors, distributor problems, streatched out timing chain/belts... those are a few common rough idle issues.

Has the fuel economy gone down? Does it still have good acceleration?

Peace,

You can go to autozone.com and register for free for free online repair manual for your vehicle. Also google images have pics. There are also more manuals here:
http://manualspace.com/manual/search/89-toyota-celica-gt-repair-manual-online-pdf.htm

timing belt and yes the belt and tensioner needs changed every 60k and if its a 4cyl. the balance belt also needs replaced

yes in this case it is correct, the reason is that the water pump and the timing belt runs toghter.. you dont want to change one without the other..

i would double check my timing. make sure crank is tdc and cam mark is lined up. if so double check any connectors that you might have disconected