It's not really clear on what you have done or what the previous owner did, but try these steps in this order:
1. Place bike on a stand so rear wheel can spin freely
2. Put the bike in neutral and spin the rear wheel; does it spin freely?
3. Put the bike in gear and spin rear wheel again; does it still spin?
4. If both tests above pass, then there is no obstruction in the gear box, and you need to check valve interference in the next step:
5. Put engine back together. Remove crankshaft end cover, timing mark access screw, and spark plug; turn crankshaft counterclockwise; does it turn freely through two full circles?
To answer your question, there should no play in the connecting rod, but that play will not prevent the engine from turning. However, that play may have developed due to a more serious problem, which may be the reason the engine is not turning.