It's just about possible to strip down and refurbish the door lock barrel, replacement tumblers are
available online, someone with a worn ignition barrel just removed the worst tumblers from it so the key still turned it but it did not register if all 8 points of the profile of the key were correct. An unscrupulous dealer might remove some of the tumblers from a problem door lock.
The eBay keyless units are all universal and can be set up to suit different cars at installation. Most of the wires can be ignored, e.g. you don't need it bibbing the horn, flashing the indicators and closing the windows so the simplest units are probably the best, and you won't need actuators either.
The car's white wire is temporarily grounded to unlock, the white/red is temporarily grounded to lock the central locking, so follow the set up instruction in the kit for 'pulse low' or 'negative trigger'.
Probably best to get someone to install this if you don't want the hassle, it's doable but awkward.
As an example (but not necessarily the same colours as any given kit):
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TG