It can take a moment or so for the transitions to appear the first time you use the program.
If you're not seeing them after a minute, though, something isn't right on your computer.
What operating system are you running? If it is a Windows Machine, have you manually gone to Windows Update and ensured you have even the non-critical updates (which don't install automatically?
How fast is your processor, how much RAM do you have and how much free, clean, freshly defragmented space is on your C or main drive?
What model of camcorder is your video coming from and what format and resolution is it?
When you started your Premiere Elements project, which settings did you select? If you've selected the correct settings for your video, there should be NO red lines above your clips when you add them to your timeline. Is that the case in your project?
Also, Transiton display is heavily video-intensive, and several users have "lost" the display of Transitions, when their video driver has been corrupted, or has become obsolete.
I would go to either the nVidia, or ATI/AMD Web site, plug in your video card, then your OS, and check for a newer video driver. Note: if you have a Dell, Lenovo, HP, or one of a few computer mfgr's. product, check out their site for a newer video driver.
Do NOT trust Windows to tell you if you have the latest driver, as that will be at least 6 mos. wrong, or about 6 versions old. Same for most driver update utilities - go to the source and check for the updated video driver.
It looks like you replied via e-mail, and for whatever reason, your Reply did not post. Unfortunately, when that happens with an e-mail response, the poster is usually totally unaware that the text is missing.
Maybe access the forum via a Web browser, and add your Reply from there.