Symptoms still not clear to me. Are you saying that it used to start OK every few days but battery eventually went flat, with new battery (less than a week old) it cranks over but fails to start, battery becomes flat, try to jump start, cranks over again but still fails to start? If so, the problem is probably spark or fuel missing.
You've caned the new battery (which now needs recharging) but if it cranks at a reasonable speed either with own battery or via jump leads, it's likely that the earth to engine/gearbox is OK and the starter is OK and the battery is OK. The earth from battery to inner wing would be worth checking as that supplies return path for just about everything except starter and alternator.
Don't consider the alternator until you get the engine running. Then if the battery warning light stays on you may have an alternator problem.
red