Welcome to the forum.
Forcing them will do more harm than good. You will need to remove the painted cover first. This will reveal the amount of crud that has built up around the operating mechanism, all of which needs to be cleaned out.
Lubricate on completion of cleaning and you should be ok.
You would need to remove the trim panel to get in there properly, as per the picture.
If that doesn’t solve the noise then you can get replacements for them.
In behind that grill is the air sensor and fan. Generally, the reason for the buzzing is a build up of dust.
Try a squirt of compressed air from one of those computer cleaning cans.
That circuit board has burnt out, that’s the black bits. As far as I’m aware, they do not supply the circuit board separately.
As long as you find the whole console from the same model car, it will simply be plug and play.
Keep your battery above 12.4v at all times and you’ll suffer less problems. If you don’t drive the car often then, as suggested above, a CTEK maintainer is the way to go.
You have got something wrong with your car. Either a failing battery or more likely, a parasitic draw.
A maintainer will only mask the problem, though still a good idea to get one.
If you continue to keep your battery at between 11.9v and 12.4v then I’m afraid you will be replacing it every 2 to 3 years. At 12.4v the battery starts to sulphate and that is what strangles the life out of it.
Keep the battery fully charged at 12.8v by using a maintainer and you’ll have far less problems.
You’re not likely to get an answer on a 8 year old thread.
Here is a link to the ones I bought,
https://www.ebay.co.uk/itm/20x-ALLOY-WHEEL-NUTS-JAGUAR-S-TYPE-X-TYPE-CHROME-LUG-BOLT-STUD-QUALITY-20L/322551270259?_trkparms=aid%3D111001%26algo%3DREC.SEED%26ao%3D1%26asc%3D20160908105057%26meid%3D279707e90cd84407af62051fd274c338%26pid%3D100675%26rk%3D1%26rkt%3D15%26mehot%3Dpp%26sd%3D322551270259%26itm%3D322551270259%26pmt%3D1%26noa%3D1%26pg%3D2481888&_trksid=p2481888.c100675.m4236&_trkparms=pageci%3A31c8544d-e131-11e9-8a5f-74dbd180d657|parentrq%3A731334ab16d0a4b7b67e7f6dff7a4b99|iid%3A1
Welcome to the forum. This is the electrical manual for your car, scroll down to page 23.
http://www.jagrepair.com/images/AutoRepairPhotos/jagxk2003.pdf