The cam belt will NOT be the reason its got no acceleration. Its a fixed item that has to be replaced either in terms of years or miles.70,000 is my understanding.
I came across this Fiat chart:
http://fiat.mopar.eu/contents/brand...elt_replacement/timing-belt-leaflets-fiat.pdf which substantiates your 70,000 mile recommendation but if you look in the very small print at the bottom you'll see it details a 5 year maximum interval if you don't reach that mileage first. In fact it also says every 4 years if the car is used under "demanding conditions" which they detail as Cold climate, City traffic, Long idling. I would guess you can add a lot of stop start to that if your car does that. Personally, unless I was doing a lot of long distance motorway cruising, which, perhaps surprisingly, is less stressful for the belt, I'd be nervous about going out to 70,000 miles - hence setting my own 5 year/60,000 mile max but starting to think of doing it at the first convenient opportunity after she turns 40,000/4years. As I do all these sort of things myself I prefer to wait for good weather and, of course I'm not paying labour charges.
Can I also recommend that you get a full kit fitted when you do it. Some will quote for the belt and it's tensioning idler without the water pump. My local Fiat main dealer does this which makes his quote look quite reasonable. However the water pump on these engines is driven by this belt - not the fan belt - so if the water pump bearing fails the "games up the pole" as we used to say as kids. I found the main dealer's menu pricing lists the water pump change as a separate job, even though a large part of the labour is the same whether the pump is done or not so if you ask the main agent to do the pump too the price shoots up to a ridiculous extent. Best option up here with us is one of the local independents who specialize in Fiats - I know of three in the Edinburgh area - But this is a relatively easy belt to do so I would be confident any competent small concern should be able to do it successfully.
One last wee thing to be aware of. Sometimes after the job is done you'll find the engine warning light illuminating. People report that, in this particular circumstance, when interrogated with a code reader/scanner it will come up with codes related to missfires. Of course there might be a relevant problem to investigate but it is likely that the engine ECU needs to relearn the new position of the camshaft sensor in relation to the crankshaft sensor which is caused by the new belt now fitted. The cure is very simple to perform, It's called a "phonic wheel relearn". There's lots on the forum about this. Sometimes you will need to reset the ECU before performing the procedure and this can only be done with the Fiat dealer tool or
Multiecuscan which is a PC based tool (and a jolly good one too - look at the Gendan website for more info on it if you want to know more. Because of this a Fiat specializing indy might be your best bet as they should know about this and have the gear needed to do it.
From what you are saying it sounds like she just needs a jolly good service and a large dose of TLC. As said above, changing the timing belt will have no effect on performance (unless the one she's running with right now is incorrectly timed?) but If you've no evidence of one having been done fairly recently I'd just renew it anyway. Whenever I, or any family member, buys a vehicle, if there is no definite evidence of a recent belt change, I would just do one anyway - maybe incorporating it into the first service I would do on it.
Good luck
Jock