My brother has a 90 accord 2 door 2.2L that is having transmission problems. This is an intermittent problem, after you start the car the green sport light comes on in the cluster and while its still in park yo hear something like a relay clicking constantly, until you apply the brake and it stops when you put it in gear. When you take off, it stays in 2nd gear and never shifts. I have been told that this is a TCM problem and to replace it, but I am hesitant to do that without being sure. Is there a way that I can be sure that the TCM is the problem and not some solenoid or something in the tranny? Ive heard that there is a way to pull codes on the TCM without a scanner but I dont know how. Once I get the codes what code would mean I need to replace the TCM? Any help would be greatly appreciated.

Most likely you are facing transmission problem. The only way out is to get the scanner/analyser to obtain the error code.