Manual transmission blocking certain gears

[ProDigit]

On my PT Cruiser 2003 at times I can not enter a gear.

I know it's obvious when driving in 5th gear that 1st gear is protected, but I'm talking about starting in 1st gear, accelerating to about 25MPH (3k-3,5k RPM), and second gear locks; I'd have to go to third gear.
When I play around for a bit, after a while of cruising in neutral (say about 5 seconds), I can finally enter it into second gear. My speed would have dropped to about 22mph, and < 3k RPM.
Not very helpful if you want to depart fast.

For ordinary driving, not going above 2,5k RPM or 20mph in first gear, does not give me any issues to shift to second gear...

What could it be?

[wheelgarage]

Syncros might be going bad, low on tranny fluid or the fluid is nolonger doing the business. Change the tranny fluid and see if there is any difference.

[ProDigit]

I'll take a look at it thanks for the suggestion.
I've noted however that I DO can enter into the gear, it just requires more force to get into.
In fact at times I can not get into gear, and at other times it goes really easy, almost as if sometimes the gears don't slide into each other...

I also notice that when driving in 2nd, and 4th gear, while driving I can feel the gearstick vibrating, as if I could feel the gears rotating and gripping into each other (I only feel this when pulling the stick backwards).
I don't have that in 1st, 3rd and 5th gear (which are all gears selectable by moving the gearstick forward).

Since I never had a manual transmission before, I was a bit afraid of 'yanking' the stick (though within operating limits).

Oil can be an issue, since it has nearly 100k miles on it, and I don't know when the last oil change has been done.
What's more, recently the 'garage man' saw some oil drips on the bottom of the car, but it did not seem to be coming from the engine, as the engine oil levels all stayed at max levels.

I may indeed need to take a look at it... I have yet to find the tranny's dipstick.