I am sorry to hear about your friend's Dad.
If you are not handy with the tools or a multimeter I would advise taking the car to a roof specialist.
The issue may be something quite simple or perhaps more complex and expensive.
Where are you based?
Your bank balance would be a good starting point.
Seriously, have a search, as this subject has been covered many times.
Was the roof working when you bought the car?
I do not have time to write you an essay on this subject at the moment I am afraid, however, this should help you.
https://www.google.co.uk/search?ei=Zxy3XJDzJpSV1fAPu9eysAE&q=how+to+test+a+350Z+wideband+o2+sensor&oq=how+to+test+a+350Z+wideband+o2+sensor&gs_l=psy-ab.12...9110.9110..19192...0.0..0.78.78.1......0....1..gws-wiz.Wl8t9swhEi8
I have genuine Nissan 350Z OEM space savers in stock.
24hour/48hour shipping is not a problem but remember that it is a holiday weekend, so you will have to move fast
Firstly I would recheck for a vacuum leak and I would also check the sensor.
If the sensor is faulty I would not mess about with aftermarket sensors.
I have new genuine Nissan sensors in stock if required.
I have 3 x OEM VLSDs in stock, and 1 x Kaaz 1.5 and 1 x Kaaz 2.0 both set at 60% lock.
All in pumpkins and all ready to be dropped in.
Just drop me a PM if I can help further.
In stock at the minute and in great shape:
No breaks, cracks, repairs, oxidisation, yellowing, fogging or scratches.
Just drop me a PM if I can help further.