Agreed, and the Beomaster even has RCA connectors, so using a "foreign" CD will be easy without needing any adapters (you'll need to use the Tape2 RCA connectors instead of proper AUX/CD though, as that only has a DIN connector).
Every unit is most probably repairable, but if the CD has mechanical damage that needs spare parts, you'd need a donor unit and it may be easier to just buy one that works in the first place. These are probably the cheapest B&O CD players.
Is your record player a Beogram 5000 or 5005, and what's wrong with it? Both are fine decks and well worth repairing. If the pickup/stylus is damaged (which it might well be due to just old age), it will cost a bit though.