There is a very good chance that both of your scopes can be repaired. It will take some effort and learning on your part, but there is a wealth of resources on the internet for repairing old Tek scopes.
Get the service manual for your models, if you don't already have it. Two possible sources:
KO4BB and
BAMA. If you find the free versions to be incomplete or hard to read,
Artek Media has better copies with higher resolution and bookmarked table-of-contents for a small price.
Read the Tektronix manual
Troubleshooting Your Oscilloscope. This was written by the folks who designed your scope. They know what they're talking about. More so than me.
Join the
Tekscopes Yahoo Group. People that collect and repair vintage Tek hang out there.
This bears repeating: first order of business on either scope is to check power supplies and fuses. IIRC, the 465B has at least three PCB-mounted ones in the corner near the power transformer. If you find a blown fuse, don't just replace the fuse, check those rails with an ohm-meter, you may find a shorted tantalum capacitor, or a shorted semiconductor. Then check all power supply rails for correct DC level and lack of ripple. You can use a decent DMM for that. The service manual will tell you exactly how close each supply should be to its labeled value. Re-check those test points with the DMM set for AC volts. A scope is the better tool here, but if you get a significant reading on the DMM you may have a bad electrolytic filter cap.
On the 465: if your tube lights up, this is good, it means you have high voltage and a beam
somewhere. From your description, it's off to the side, which indicates a horizontal deflection fault, as noted earlier. X-Y mode disables the sweep, so that will tell you whether to go for the sweep generator or the horizontal deflection amp. The amp seems more likely, and the outputs, as duffy said, are good suspects. Oh, and the transistors are all socketed on the 465B, so give everything a good wiggle. You may get lucky.
If you decide to dive in, don't forget to be mindful of the high voltages present in some areas. This includes not only the obvious CRT circuits but the deflection finals as well. It can destroy test equipment, and it can destroy you too!