So some of this depends quite heavily on the period, but here are a few things to start your thinking. Besides those, a few other things:

While our understanding of the place of patronage has evolved quite a lot from the days of Gelzer's monumental study it's certainly true that a person who didn't have someone on whom he could rely was going to have a hard time of just about everything. Whether one's patron consisted of a real bigshot or just a local magister vici or something didn't matter much. Roman society depended down to the lowest levels on mutual reciprocity, and ties like this were what kept things revolving. This of course means that someone with no attachments whatsoever, who might as well have not existed as far as Roman society was concerned, would have little recourse, but I don't think this should be particularly unexpected. The concept of investigative police is quite a new one, as is public prosecution.

The army should not be understood as a police force. The military and quasi-military (e.g. vigiles) contingents allowed to operate daily within the city were not there to investigate or prevent crime, they were there for the sole function of maintaining public order. The praetorians and urbans existed within the city for no other purpose than to violently put down public disturbances against the state and the person of the princeps. They existed as a militarized public order force, little more. Prior to the Principate no such force existed. Magistrates might individually attempt to exercise public order, and laws against vis increasingly appeared in the Republican state, but such measures were often ineffective or were surfaced to combat particular incidents and trends, not as general methods of maintaining state order. Indeed, when Pompey marched his troops into the city to violently put down the riots that followed Publius Clodius' death he was reviled and suspected of aiming at dictatorial powers--in the event he did succeed in obtaining the sole consulship