ArcMap is able to align layers that have different coordinate systems. So transforming coordinate system is not the correct direction to fix problem. Before you start trying to fix the problem, it is important to understand the following concepts
Coordinate system and Projection: the term coordinate system refers to the coordinates expressed in decimal degrees (i.e., geographic coordinate system) or the coordinates expressed in meters or feet (i.e., projected coordinate system). The term projection is an older term that is also used, but it is not as precise
Native coordinate system: all GIS data are collected, created or derived in a coordinate system which is called the native coordinate system. The native coordinate system is either stored in the data or recorded somewhere else (e.g., metadata, document or device such as GPS).
Define coordinate system: The coordinate system information, such as projection parameters, datum and spheroid, needs to be recorded for the layers such that ArcGIS can recognize the layers’ coordinate systems. The process of recording coordinate system using ArcGIS tool or other tools is called defining coordinate system.
On-the-fly projection: ArcGIS can display layer stored in one coordinate system as if it were in another coordinate system. This is called on-the-fly projection. ArcGIS automatically integrates layers whose coordinate systems are well defined by projecting your data on the fly for visualizing, mapping, analysis, and so forth. Therefore, the layers’ coordinate systems need not be the same to align in ArcMap. The on-the-fly projection is used for display and query purposes only; the actual data is not altered.
Data frame coordinate system: to display your data correctly, a data frame uses a coordinate system. This can be any coordinate system ArcGIS supports. Data frame’s coordinate system needs not be the same as that of the layers. On-the-fly projection, in fact, means that ArcMap projects all the layers to the data frame’s coordinate system.
Layers do not line up in ArcMap is because ArcMap is not able to project all layers on the fly correctly. The reasons for this might be
one or more layers have incorrectly defined coordinate system
Check the data frame coordinate system. When ArcMap is started with a new, empty map, the coordinate system for the default data frame is not defined. The first layer added to an empty data frame sets the coordinate system for the data frame. If the first layer has an undefined coordinate system, the data frame coordinate system is set to Unknown. The layers added subsequently will not be projected on the fly and will be displayed in its native coordinate system. Even if you removed the first layer from the table of content, the coordinate system of data frame is still set as undefined. You can define the coordinate system for data frame in two ways:
You can use the Data Frame Properties dialog box to set or change the coordinate system. If you change the data frame's coordinate system, all layers that have coordinate systems will be projected on the fly to the new coordinate system.
Start a new, empty data frame and add a layer with a defined coordinate system. ArcMap will automatically set the data frame's coordinate system to be the same as that of the layer. The layers added subsequently will be automatically projected to the data frame’s coordinate system as long as they have defined coordinate systems.
Check the layer coordinate systems. ArcMap will not project data on the fly if the coordinate system for the layer has not been defined. Therefore, you should check if all the layers have the defined coordinate systems. The methods to detect the unknown coordinate system include
In the table of content, right click the layer name, click properties, and click the Source tab in the Layer Properties dialog box. If the layer doesn't have a coordinate system defined, the coordinate system will be listed as Unknown on the dialog box as shown in Figure 2. In this case, you need to identify and define the coordinate systems for the layer.
If all layers have defined coordinate systems as shown in Figure 3 but the layers do not line up, one or more layers must have used wrong coordinate systems. You need to find the correct coordinate system (step 6) and modify the definition.
Identify unknown coordinate system for layers. Usually you can obtain the coordinate system information from the data source (metadata or GIS staff). In case you are not able to obtain the coordinate system information from the data source, ArcGIS 9.3 online help document Identifying an unknown coordinate system described the techniques to find the correct coordinate system. But the investigation process might be tedious.