Capacity is not the issue - ALL SATA systems (drives and controllers) support "48-bit LBA" that limits the disk size up in the petabyte region, however huge that is.
I see two possibilities. One is hardware-related. Most SATA II drives can switch to the 150 speed when connected to an original SATA controller. For those that don't, many drive manufacturers provided a way to force it to limit itself to the slower speed. Seagate does this with a jumper block; in fact, many of their drives arrive with a jumper installed to impose this limit by default, and anyone using them on a system known to support the faster speed is supposed to remove that jumper. Others do this differently - I saw one manufacturer that did it with utility software to set a parameter in the HDD's own controller board.
The other real possibility is that you did not do the proper software setup of your new drive. When you say the drive "is not detected by my computer ", exactly how do you know this. If you just plugged in the new drive, booted and looked for it in My Computer, it will not be there. However, if you then check in Disk Manager it probably is there but not yet ready for Windows to use. Click on Start in the lower left, then in that main pop-up menu RIGHT-click on My Computer and choose from that menu "Manage". In the left panel of the resulting window expand "Storage" if necessary and click on "Disk Management". You will get two scrollable windows on the right. The top one shows you all the disks Windows is using now. The bottom one includes those hardware devices plus any others Windows does not yet know how to use. I'm guessing your new drive is there as an empty block.
Before Windows can use a new blank disk, two operations have to be done on it: Partition, and Format that partition. Usually the easiest way to do this is to use a utility for that purpose supplied for free by the disk manufacturer. It may be on a CD that came with your HDD unit. If not, go the the manufacturer's website and look for downloadable software to Install a new disk. Seagate calls theirs Disk Wizard, WD has Data Lifeguard, others have theirs. You download and install the tools on your existing drive, then run them to prepare you new disk. MAKE SURE YOU PICK ONLY THE NEW DISK to operate on - these steps completely destroy any previous data on the disk and it cannot be recovered! Watch for choices to make as you go through the menu system. You probably want this new drive to be used as one large volume with all of the disk's space (as opposed to making separate smaller Partitions), you do NOT want it to be bootable since it will be just a data storage drive, and you should choose the NTFS file System. Once your choices are made the software will set up the new drive. Then you reboot so Windows can see it and it will show up in My Computer ready to use.
If you cannot get manufacturer's free utilities to do this job for you, Disk Manager also has the tools. You start by RIGHT-clicking on the empty block in the lower right, and from that menu choose to Create a new Primary Partition. Set its size to the max (full drive space) unless you want something else, and make it not bootable. When it finishes making the Partition, RIGHT-click on that and choose to Format it, installing the NTFS File System. For most situations, choose to do a Quick Format - it does all the essentials and you will be finished. Again, you reboot and Windows will have the drive ready to use. You do have the option to choose instead a Full Format. That does the Quick version, then does a complete testing of the entire drive to detect any possible errors and mark then unusable. This is usually unnecessary with a new drive, but you can do it if you want. Just allow lots of time - we did one recently on a 1.5 TB drive and it took 5 hours.