Ghengis has pretty much hit the nail on the head here:
Every part must be treated as suspect, huge amounts of bonding, painting, etc. to be removed and redone (much harder than doing from new). Far greater depth and rigour of inspection and NDT than I'd expect on newly made parts.
So for a warbird, lets say a Vampire 1950's jet, to get to flying status
Wooden Fuselage, depending on how the a/c has been stored, has the wood rotted? If so how much? Has it/is it, delaminating? is it still possible to get a similar type of wood and treated appropriately that can do the job. If not where do you get it? Whom can supply the relatively small batch you'd need. Assuming yes, who can do the repair to a required standard?
Aluminium/Alloy wings, How much corrosion has occurred? If taking a panel off and it fails inspection, where do you get the correct spec material from to replace it? When it arrives who has the skill to cut/form/treat the metal to the final spec?.
Okay now we're on the wings, get the rubber fuel cells out, have they perrished?, if so who can make new ones?, same for the tyres, where do you get stock for a 50 yr old aircraft. Some Mfg people can make batches for operators, but the small production runs and design process can make them very expensive indeed. Hydraulics/electrics are similar, a key element is that aircraft are not built in the same number that road vehicles generally are, so you cannot get the interchangeability that you may get with the benefit of similar road vehicles. Instrumentation/transparencies, finding stock or remanufacturing is a real challege. An area lacking in aviation nowadays is engineering skills, I think the average age of an aircraft engineer is well into his 40's. There are very few people with the appropriate skills nowadays, so if you're not doing everything yourself, you'll have to potentially pay the going rate. Arguably for road vehicles you could change materials without too much problem. with an aircraft it not possible or needs certifying. What a lot of what you pay for is the skill, and somewhere to do it, (hangers aren't cheap).