I have had my car for 4 years now. It is a Ford fiesta 2007 with 95,000 miles and is manual transmission. I usually drive it every single day for about 30 mins, just doing errands, but with lockdown this winter I haven't had as many places to go. When I got back from Christmas holidays the car simply would not start, so I ran the battery through and it was low on charge, so I got a new battery. This sort of fixed the problem, but since then it sometimes turns on, and sometimes it just turns over. The engine always cranks, there is never just a clicking sound. So if I'm right in my deductions, then it shouldn't really be the battery or the starter. 

I took the car to the garage this week and the mechanic said that he thinks there is an issue of connection between the key and the engine. So I tried my spare key, and without fail, every single time the engine will crank if in neutral but not turn on, and will turn on straight away without fail if in first gear. 

Apparently the car did something similar to this last winter with my mum, but by spring-time I was home and drove it and didn't notice any issues. 

Any ideas?

Thank you so much!